View source for Machine learning

{{Short description|Study of algorithms that improve automatically through experience}}
{{Machine learning bar}}
{{Artificial intelligence|Major goals}}

'''Machine learning''' ('''ML''') is a field of study in [[Artificial intelligence|artificial intelligence]] concerned with the development and study of [[Computational statistics|statistical algorithms]] that can learn from data and generalize to unseen data, and thus perform tasks without explicit instructions.{{refn|The definition "without being explicitly programmed" is often attributed to [[Biography:Arthur Samuel (computer scientist)|Arthur Samuel]], who coined the term "machine learning" in 1959, but the phrase is not found verbatim in this publication, and may be a paraphrase that appeared later. Confer "Paraphrasing Arthur Samuel (1959), the question is: How can computers learn to solve problems without being explicitly programmed?" in {{Cite conference |chapter=Automated Design of Both the Topology and Sizing of Analog Electrical Circuits Using Genetic Programming |conference=Artificial Intelligence in Design '96 |last1=Koza |first1=John R. |last2=Bennett |first2=Forrest H. |last3=Andre |first3=David |last4=Keane |first4=Martin A. |title=Artificial Intelligence in Design '96 |date=1996 |publisher=Springer, Dordrecht |pages=151–170 |language=en |doi=10.1007/978-94-009-0279-4_9 |isbn=978-94-010-6610-5 }}}} Recently, generative [[Artificial neural network|artificial neural network]]s have been able to surpass many previous approaches in performance.<ref name="ibm">{{Cite web |title=What is Machine Learning? |url=https://www.ibm.com/topics/machine-learning |access-date=2023-06-27 |website=IBM |language=en-us}}</ref><ref name=":6">{{Cite web |last=Zhou |first=Victor |date=2019-12-20 |title=Machine Learning for Beginners: An Introduction to Neural Networks |url=https://towardsdatascience.com/machine-learning-for-beginners-an-introduction-to-neural-networks-d49f22d238f9 |url-status=live |access-date=2021-08-15 |website=Medium |language=en |archive-date=2022-03-09 |archive-url=https://web.archive.org/web/20220309053518/https://towardsdatascience.com/machine-learning-for-beginners-an-introduction-to-neural-networks-d49f22d238f9 }}</ref>

Machine learning approaches have been applied to many fields including [[Large language model|large language model]]s, [[Computer vision|computer vision]], [[Speech recognition|speech recognition]], [[Email filtering|email filtering]], [[Earth:Agriculture|agriculture]], and medicine, where it is too costly to develop algorithms to perform the needed tasks.<ref name="tvt">{{Cite journal |last1=Hu |first1=Junyan |last2=Niu |first2=Hanlin |last3=Carrasco |first3=Joaquin |last4=Lennox |first4=Barry |last5=Arvin |first5=Farshad |date=2020 |title=Voronoi-Based Multi-Robot Autonomous Exploration in Unknown Environments via Deep Reinforcement Learning |journal=IEEE Transactions on Vehicular Technology |volume=69 |issue=12 |pages=14413–14423 |doi=10.1109/tvt.2020.3034800 |s2cid=228989788 |issn=0018-9545 |doi-access=free }}</ref><ref name=":7">{{cite journal |last1=Yoosefzadeh-Najafabadi|first1=Mohsen |last2=Hugh |first2=Earl |last3=Tulpan |first3=Dan |last4=Sulik |first4=John |last5=Eskandari |first5=Milad |title=Application of Machine Learning Algorithms in Plant Breeding: Predicting Yield From Hyperspectral Reflectance in Soybean? |journal=Front. Plant Sci. |volume=11 |year=2021 |pages=624273|doi=10.3389/fpls.2020.624273 |pmid=33510761 |pmc=7835636 |doi-access=free }}</ref> ML is known in its application across business problems under the name [[Predictive analytics|predictive analytics]]. Although not all machine learning is statistically based, [[Computational statistics|computational statistics]] is an important source of the field's methods.

The mathematical foundations of ML are provided by [[Mathematical optimization|mathematical optimization]] (mathematical programming) methods. [[Data mining]] is a related (parallel) field of study, focusing on [[Exploratory data analysis|exploratory data analysis]] through [[Unsupervised learning|unsupervised learning]].{{refn|Machine learning and pattern recognition "can be viewed as two facets of the same field".<ref name="bishop2006" />{{rp|vii}}}}<ref name=":9">{{cite journal |last=Friedman |first=Jerome H. |title=Data Mining and Statistics: What's the connection? |journal=Computing Science and Statistics |volume=29 |issue=1 |year=1998 |pages=3–9}}</ref> From a theoretical point of view [[Probably approximately correct learning]] provides a framework for describing machine learning.

{{Toclimit|3}}

== History and relationships to other fields ==
The term ''machine learning'' was coined in 1959 by [[Biography:Arthur Samuel (computer scientist)|Arthur Samuel]], an [[Company:IBM|IBM]] employee and pioneer in the field of computer gaming and [[Artificial intelligence|artificial intelligence]].<ref name="Samuel">{{Cite journal|last=Samuel|first=Arthur|date=1959|title=Some Studies in Machine Learning Using the Game of Checkers|journal=IBM Journal of Research and Development|volume=3|issue=3|pages=210–229|doi=10.1147/rd.33.0210|citeseerx=10.1.1.368.2254|s2cid=2126705 }}</ref><ref name=":8">R. Kohavi and F. Provost, "Glossary of terms", Machine Learning, vol. 30, no. 2–3, pp. 271–274, 1998.</ref> The synonym ''self-teaching computers'' was also used in this time period.<ref name=cyberthreat>{{cite news |last1=Gerovitch |first1=Slava |title=How the Computer Got Its Revenge on the Soviet Union |url=https://nautil.us/issue/23/dominoes/how-the-computer-got-its-revenge-on-the-soviet-union |access-date=19 September 2021 |work=Nautilus |date=9 April 2015 |archive-date=22 September 2021 |archive-url=https://web.archive.org/web/20210922175839/https://nautil.us/issue/23/Dominoes/how-the-computer-got-its-revenge-on-the-soviet-union |url-status=dead }}</ref><ref>{{cite journal |last1=Lindsay |first1=Richard P. |title=The Impact of Automation On Public Administration |journal=Western Political Quarterly |date=1 September 1964 |volume=17 |issue=3 |pages=78–81 |doi=10.1177/106591296401700364 |s2cid=154021253 |url=https://journals.sagepub.com/doi/10.1177/106591296401700364 |access-date=6 October 2021 |language=en |issn=0043-4078 |archive-date=6 October 2021 |archive-url=https://web.archive.org/web/20211006190841/https://journals.sagepub.com/doi/10.1177/106591296401700364 |url-status=live }}</ref>

Although the earliest machine learning model was introduced in the 1950s when [[Biography:Arthur Samuel (computer scientist)|Arthur Samuel]] invented a program that calculated the winning chance in checkers for each side, the history of machine learning roots back to decades of human desire and effort to study human cognitive processes.<ref name=":02">{{Cite web |title=History and Evolution of Machine Learning: A Timeline |url=https://www.techtarget.com/whatis/A-Timeline-of-Machine-Learning-History |access-date=2023-12-08 |website=WhatIs |language=en}}</ref> In 1949, Canadian psychologist [[Biography:Donald O. Hebb|Donald Hebb]] published the book ''The Organization of Behavior'', in which he introduced a [[Hebbian theory|theoretical neural structure]] formed by certain interactions among nerve cells.<ref>{{Cite journal |last=Milner |first=Peter M. |date=1993 |title=The Mind and Donald O. Hebb |url=https://www.jstor.org/stable/24941344 |journal=Scientific American |volume=268 |issue=1 |pages=124–129 |doi=10.1038/scientificamerican0193-124 |jstor=24941344 |pmid=8418480 |bibcode=1993SciAm.268a.124M |issn=0036-8733}}</ref> Hebb's model of neurons interacting with one another set a groundwork for how AIs and machine learning algorithms work under nodes, or artificial neurons used by computers to communicate data.<ref name=":02" /> Other researchers who have studied human cognitive systems contributed to the modern machine learning technologies as well, including logician [[Biography:Walter Pitts|Walter Pitts]] and Warren McCulloch, who proposed the early mathematical models of neural networks to come up with algorithms that mirror human thought processes.<ref name=":02" />

By the early 1960s an experimental "learning machine" with [[Punched tape|punched tape]] memory, called Cybertron, had been developed by [[Company:Raytheon Company|Raytheon Company]] to analyze sonar signals, electrocardiograms, and speech patterns using rudimentary [[Reinforcement learning|reinforcement learning]]. It was repetitively "trained" by a human operator/teacher to recognize patterns and equipped with a "[[Goof|goof]]" button to cause it to re-evaluate incorrect decisions.<ref>"Science: The Goof Button", {{wipe|Time (magazine)}}, 18 August 1961.
</ref> A representative book on research into machine learning during the 1960s was Nilsson's book on Learning Machines, dealing mostly with machine learning for pattern classification.<ref>Nilsson N. Learning Machines, McGraw Hill, 1965.</ref> Interest related to pattern recognition continued into the 1970s, as described by Duda and Hart in 1973.<ref>Duda, R., Hart P. Pattern Recognition and Scene Analysis, Wiley Interscience, 1973</ref> In 1981 a report was given on using teaching strategies so that a [[Neural network|neural network]] learns to recognize 40 characters (26 letters, 10 digits, and 4 special symbols) from a computer terminal.<ref>S. Bozinovski "Teaching space: A representation concept for adaptive pattern classification" COINS Technical Report No. 81-28, Computer and Information Science Department, University of Massachusetts at Amherst, MA, 1981. https://web.cs.umass.edu/publication/docs/1981/UM-CS-1981-028.pdf {{Webarchive|url=https://web.archive.org/web/20210225070218/https://web.cs.umass.edu/publication/docs/1981/UM-CS-1981-028.pdf |date=2021-02-25 }}</ref>

[[Biography:Tom M. Mitchell|Tom M. Mitchell]] provided a widely quoted, more formal definition of the algorithms studied in the machine learning field: "A computer program is said to learn from experience ''E'' with respect to some class of tasks ''T'' and performance measure ''P'' if its performance at tasks in ''T'', as measured by ''P'',  improves with experience ''E''."<ref name="Mitchell-1997">{{cite book
|author=Mitchell, T. 
|title=Machine Learning
|publisher=McGraw Hill
|isbn= 978-0-07-042807-2
|pages=2

Modern-day machine learning has two objectives, one is to classify data based on models which have been developed, the other purpose is to make predictions for future outcomes based on these models. A hypothetical algorithm specific to classifying data may use computer vision of moles coupled with supervised learning in order to train it to classify the cancerous moles. A machine learning algorithm for stock trading may inform the trader of future potential predictions.<ref>{{Cite web|date=2020-12-08|title=Introduction to AI Part 1|url=https://edzion.com/2020/12/09/introduction-to-ai-part-1/|access-date=2020-12-09|website=Edzion|language=en|archive-date=2021-02-18|archive-url=https://web.archive.org/web/20210218005157/https://edzion.com/2020/12/09/introduction-to-ai-part-1/|url-status=live}}</ref>

=== Artificial intelligence ===
[[File:AI hierarchy.svg|thumb|Machine learning as subfield of AI<ref name="journalimcms.org">{{cite journal |vauthors=Sindhu V, Nivedha S, Prakash M |date=February 2020|title=An Empirical Science Research on Bioinformatics in Machine Learning |journal=Journal of Mechanics of Continua and Mathematical Sciences |issue=7 |doi=10.26782/jmcms.spl.7/2020.02.00006 |doi-access=free}}</ref>]]
As a scientific endeavor, machine learning grew out of the quest for [[Artificial intelligence|artificial intelligence]] (AI). In the early days of AI as an [[Discipline (academia)|academic discipline]], some researchers were interested in having machines learn from data. They attempted to approach the problem with various symbolic methods, as well as what were then termed "[[Neural network|neural network]]s"; these were mostly [[Perceptron|perceptron]]s and [[ADALINE|other models]] that were later found to be reinventions of the [[Generalized linear model|generalized linear model]]s of statistics.<ref>{{cite book |last1=Sarle |first1=Warren S.|chapter=Neural Networks and statistical models |pages=1538–50 |year=1994 |title=SUGI 19: proceedings of the Nineteenth Annual SAS Users Group International Conference |publisher=SAS Institute |isbn=9781555446116 |oclc=35546178}}</ref> Probabilistic reasoning was also employed, especially in automated medical diagnosis.<ref name="aima">{{cite AIMA|edition=2}}</ref>{{rp|488}}

However, an increasing emphasis on the logical, knowledge-based approach caused a rift between AI and machine learning. Probabilistic systems were plagued by theoretical and practical problems of data acquisition and representation.<ref name="aima" />{{rp|488}} By 1980, [[Expert system|expert system]]s had come to dominate AI, and statistics was out of favor.<ref name="changing">{{Cite journal | last1 = Langley | first1 = Pat| title = The changing science of machine learning | doi = 10.1007/s10994-011-5242-y | journal = Machine Learning| volume = 82 | issue = 3 | pages = 275–9 | year = 2011 | doi-access = free }}</ref> Work on symbolic/knowledge-based learning did continue within AI, leading to [[Inductive logic programming|inductive logic programming]], but the more statistical line of research was now outside the field of AI proper, in [[Pattern recognition|pattern recognition]] and [[Information retrieval|information retrieval]].<ref name="aima" />{{rp|708–710; 755}} Neural networks research had been abandoned by AI and [[Computer science|computer science]] around the same time. This line, too, was continued outside the AI/CS field, as "[[Connectionism|connectionism]]", by researchers from other disciplines including [[Biography:John Hopfield|Hopfield]], [[Biography:David Rumelhart|Rumelhart]], and Hinton. Their main success came in the mid-1980s with the reinvention of [[Backpropagation|backpropagation]].<ref name="aima" />{{rp|25}}

Machine learning (ML), reorganized and recognized as its own field, started to flourish in the 1990s. The field changed its goal from achieving artificial intelligence to tackling solvable problems of a practical nature. It shifted focus away from the [[Symbolic artificial intelligence|symbolic approaches]] it had inherited from AI, and toward methods and models borrowed from statistics, [[Fuzzy logic|fuzzy logic]], and [[Probability theory|probability theory]].<ref name="changing" />

=== Data mining ===
Machine learning and [[Data mining|data mining]] often employ the same methods and overlap significantly, but while machine learning focuses on prediction, based on ''known'' properties learned from the training data, [[Data mining|data mining]] focuses on the [[Philosophy:Discovery (observation)|discovery]] of (previously) ''unknown'' properties in the data (this is the analysis step of knowledge discovery in databases). [[Data mining]] uses many machine learning methods, but with different goals; on the other hand, machine learning also employs data mining methods as "[[Unsupervised learning|unsupervised learning]]" or as a preprocessing step to improve learner accuracy. Much of the confusion between these two research communities (which do often have separate conferences and separate journals, ECML PKDD being a major exception) comes from the basic assumptions they work with: in machine learning, performance is usually evaluated with respect to the ability to ''reproduce known'' knowledge, while in knowledge discovery and data mining (KDD) the key task is the discovery of previously ''unknown'' knowledge. Evaluated with respect to known knowledge, an uninformed (unsupervised) method will easily be outperformed by other supervised methods, while in a typical KDD task, supervised methods cannot be used due to the unavailability of training data.

Machine learning also has intimate ties to [[Mathematical optimization|optimization]]: many learning problems are formulated as minimization of some [[Loss function|loss function]] on a training set of examples. Loss functions express the discrepancy between the predictions of the model being trained and the actual problem instances (for example, in classification, one wants to assign a label to instances, and models are trained to correctly predict the pre-assigned labels of a set of examples).<ref>{{cite encyclopedia |last1=Le Roux |first1=Nicolas |first2=Yoshua |last2=Bengio |first3=Andrew |last3=Fitzgibbon |title=Improving First and Second-Order Methods by Modeling Uncertainty |encyclopedia=Optimization for Machine Learning |year=2012 |page=404 |editor1-last=Sra |editor1-first=Suvrit |editor2-first=Sebastian |editor2-last=Nowozin |editor3-first=Stephen J. |editor3-last=Wright |publisher=MIT Press |url=https://books.google.com/books?id=JPQx7s2L1A8C&q=%22Improving+First+and+Second-Order+Methods+by+Modeling+Uncertainty&pg=PA403 |isbn=9780262016469 |access-date=2020-11-12 |archive-date=2023-01-17 |archive-url=https://web.archive.org/web/20230117053335/https://books.google.com/books?id=JPQx7s2L1A8C&q=%22Improving+First+and+Second-Order+Methods+by+Modeling+Uncertainty&pg=PA403 |url-status=live }}</ref>

=== Generalization ===
The difference between optimization and machine learning arises from the goal of [[Philosophy:Generalization (learning)|generalization]]: while optimization algorithms can minimize the loss on a training set, machine learning is concerned with minimizing the loss on unseen samples. Characterizing the generalization of various learning algorithms is an active topic of current research, especially for [[Deep learning|deep learning]] algorithms.

=== Statistics ===
Machine learning and [[Statistics|statistics]] are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population [[Statistical inference|inferences]] from a [[Sample (statistics)|sample]], while machine learning finds generalizable predictive patterns.<ref>{{cite journal |first1=Danilo |last1=Bzdok |first2=Naomi |last2=Altman |first3=Martin |last3=Krzywinski |title=Statistics versus Machine Learning |journal=[[Nature Methods]] |volume=15 |issue=4 |pages=233–234 |year=2018 |doi=10.1038/nmeth.4642 |pmid=30100822 |pmc=6082636 }}</ref> According to [[Biography:Michael I. Jordan|Michael I. Jordan]], the ideas of machine learning, from methodological principles to theoretical tools, have had a long pre-history in statistics.<ref name="mi jordan ama">{{cite web|url=https://www.reddit.com/r/MachineLearning/comments/2fxi6v/ama_michael_i_jordan/ckelmtt?context=3|title=statistics and machine learning|publisher=reddit|date=2014-09-10|access-date=2014-10-01|author=Michael I. Jordan|author-link=Michael I. Jordan|archive-date=2017-10-18|archive-url=https://web.archive.org/web/20171018192328/https://www.reddit.com/r/MachineLearning/comments/2fxi6v/ama_michael_i_jordan/ckelmtt/?context=3|url-status=live}}</ref> He also suggested the term [[Data science|data science]] as a placeholder to call the overall field.<ref name="mi jordan ama" />

Conventional statistical analyses require the a priori selection of a model most suitable for the study data set. In addition, only significant or theoretically relevant variables based on previous experience are included for analysis. In contrast, machine learning is not built on a pre-structured model; rather, the data shape the model by detecting underlying patterns. The more variables (input) used to train the model, the more accurate the ultimate model will be.<ref>Hung et al. Algorithms to Measure Surgeon Performance and Anticipate Clinical Outcomes in Robotic Surgery. JAMA Surg. 2018</ref>

[[Biography:Leo Breiman|Leo Breiman]] distinguished two statistical modeling paradigms: data model and algorithmic model,<ref name=":4">{{cite journal|url=http://projecteuclid.org/download/pdf_1/euclid.ss/1009213726|title=Breiman: Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author)|author=Cornell University Library|journal=Statistical Science|date=August 2001|volume=16|issue=3|doi=10.1214/ss/1009213726|s2cid=62729017|access-date=8 August 2015|archive-date=26 June 2017|archive-url=https://web.archive.org/web/20170626042637/http://projecteuclid.org/download/pdf_1/euclid.ss/1009213726|url-status=live|doi-access=free}}</ref> wherein "algorithmic model" means more or less the machine learning algorithms like [[Random forest|Random Forest]].

Some statisticians have adopted methods from machine learning, leading to a combined field that they call ''statistical learning''.<ref name="islr">{{cite book |author1=Gareth James |author2=Daniela Witten |author3=Trevor Hastie |author4=Robert Tibshirani |title=An Introduction to Statistical Learning |publisher=Springer |year=2013 |url=http://www-bcf.usc.edu/~gareth/ISL/ |page=vii |access-date=2014-10-25 |archive-date=2019-06-23 |archive-url=https://web.archive.org/web/20190623150237/http://www-bcf.usc.edu/~gareth/ISL/ |url-status=live }}</ref>

===Statistical Physics===
Analytical and computational techniques derived from deep-rooted physics of disordered systems can be extended to large-scale problems, including machine learning, e.g., to analyze the weight space of deep neural networks.<ref name=SP_1>{{cite journal| author1=Ramezanpour, A.| author2=Beam, A.L.| author3=Chen, J.H.| author4=Mashaghi, A.| title=Statistical Physics for Medical Diagnostics: Learning, Inference, and Optimization Algorithms| journal=Diagnostics| date=17 November 2020| volume=10| issue=11| page=972| doi=10.3390/diagnostics10110972| doi-access=free| pmid=33228143| pmc=7699346}}</ref> Statistical physics is thus finding applications in the area of medical diagnostics.<ref name=SP_2>{{cite journal| title=Statistical physics of medical diagnostics: Study of a probabilistic model| author1=Mashaghi, A.| author2=Ramezanpour, A. | journal=[[Physics:Physical Review E|Physical Review E]]| volume=97| date=16 March 2018| issue=3–1| page=032118| doi=10.1103/PhysRevE.97.032118| pmid=29776109| arxiv=1803.10019| bibcode=2018PhRvE..97c2118M| s2cid=4955393}}</ref>

== {{anchor|Generalization}} Theory ==
{{Main|Computational learning theory|Statistical learning theory}}
A core objective of a learner is to generalize from its experience.<ref name="bishop2006">{{citation|first= C. M. |last= Bishop |year=2006 |title=Pattern Recognition and Machine Learning |publisher=Springer |isbn=978-0-387-31073-2}}</ref><ref name=":5">{{Cite Mehryar Afshin Ameet 2012}}</ref> Generalization in this context is the ability of a learning machine to perform accurately on new, unseen examples/tasks after having experienced a learning data set. The training examples come from some generally unknown probability distribution (considered representative of the space of occurrences) and the learner has to build a general model about this space that enables it to produce sufficiently accurate predictions in new cases.

The computational analysis of machine learning algorithms and their performance is a branch of [[Theoretical computer science|theoretical computer science]] known as [[Computational learning theory|computational learning theory]] via the [[Probably approximately correct learning|Probably Approximately Correct Learning]] (PAC) model. Because training sets are finite and the future is uncertain, learning theory usually does not yield guarantees of the performance of algorithms. Instead, probabilistic bounds on the performance are quite common. The bias–variance decomposition is one way to quantify generalization [[Errors and residuals|error]].

For the best performance in the context of generalization, the complexity of the hypothesis should match the complexity of the function underlying the data. If the hypothesis is less complex than the function, then the model has under fitted the data. If the complexity of the model is increased in response, then the training error decreases. But if the hypothesis is too complex, then the model is subject to [[Overfitting|overfitting]] and generalization will be poorer.<ref name="alpaydin">{{Cite book |author=Alpaydin, Ethem |title=Introduction to Machine Learning |url=https://archive.org/details/introductiontoma00alpa_0 |year=2010 |publisher=The MIT Press |place=London |isbn=978-0-262-01243-0 |access-date=4 February 2017 |url-access=registration }}</ref>

In addition to performance bounds, learning theorists study the time complexity and feasibility of learning. In computational learning theory, a computation is considered feasible if it can be done in [[Time complexity#Polynomial time|polynomial time]]. There are two kinds of [[Time complexity|time complexity]] results: Positive results show that a certain class of functions can be learned in polynomial time. Negative results show that certain classes cannot be learned in polynomial time.

== Approaches ==

{{Anchor|Algorithm types}}
Machine learning approaches are traditionally divided into three broad categories, which correspond to learning paradigms, depending on the nature of the "signal" or "feedback" available to the learning system:
* [[Supervised learning]]: The computer is presented with example inputs and their desired outputs, given by a "teacher", and the goal is to learn a general rule that [[Map (mathematics)|maps]] inputs to outputs.
* [[Unsupervised learning]]: No labels are given to the learning algorithm, leaving it on its own to find structure in its input. Unsupervised learning can be a goal in itself (discovering hidden patterns in data) or a means towards an end ([[Feature learning|feature learning]]).
* [[Reinforcement learning]]: A computer program interacts with a dynamic environment in which it must perform a certain goal (such as driving a vehicle or playing a game against an opponent). As it navigates its problem space, the program is provided feedback that's analogous to rewards, which it tries to maximize.<ref name="bishop2006"/> 
Although each algorithm has advantages and limitations, no single algorithm works for all problems.<ref>{{cite journal |last1=Jordan |first1=M. I. |last2=Mitchell |first2=T. M. |title=Machine learning: Trends, perspectives, and prospects |journal=Science |date=17 July 2015 |volume=349 |issue=6245 |pages=255–260 |doi=10.1126/science.aaa8415|pmid=26185243 |bibcode=2015Sci...349..255J |s2cid=677218 }}</ref><ref>{{cite book |last1=El Naqa |first1=Issam |last2=Murphy |first2=Martin J. |title=Machine Learning in Radiation Oncology |chapter=What is Machine Learning? |date=2015 |pages=3–11 |doi=10.1007/978-3-319-18305-3_1|isbn=978-3-319-18304-6 |s2cid=178586107 }}</ref><ref>{{cite journal |last1=Okolie |first1=Jude A. |last2=Savage |first2=Shauna |last3=Ogbaga |first3=Chukwuma C. |last4=Gunes |first4=Burcu |title=Assessing the potential of machine learning methods to study the removal of pharmaceuticals from wastewater using biochar or activated carbon |journal=Total Environment Research Themes |date=June 2022 |volume=1-2 |pages=100001 |doi=10.1016/j.totert.2022.100001|s2cid=249022386 |doi-access=free }}</ref>

=== Supervised learning ===
{{Main|Supervised learning}}
[[File:Svm max sep hyperplane with margin.png|thumb|A [[Support-vector machine|support-vector machine]] is a supervised learning model that divides the data into regions separated by a [[Linear classifier|linear boundary]]. Here, the linear boundary divides the black circles from the white.]]
Supervised learning algorithms build a mathematical model of a set of data that contains both the inputs and the desired outputs.<ref>{{cite book |last1=Russell |first1=Stuart J. |last2=Norvig |first2=Peter |title=Artificial Intelligence: A Modern Approach |date=2010 |publisher=Prentice Hall |isbn=9780136042594 |edition=Third|title-link=Artificial Intelligence: A Modern Approach }}</ref> The data is known as training data, and consists of a set of training examples. Each training example has one or more inputs and the desired output, also known as a supervisory signal.  In the mathematical model, each training example is represented by an [[Array data structure|array]] or vector, sometimes called a feature vector, and the training data is represented by a [[Matrix (mathematics)|matrix]]. Through [[Mathematical optimization#Computational optimization techniques|iterative optimization]] of an [[Loss function|objective function]], supervised learning algorithms learn a function that can be used to predict the output associated with new inputs.<ref>{{cite book |last1=Mohri |first1=Mehryar |last2=Rostamizadeh |first2=Afshin |last3=Talwalkar |first3=Ameet |title=Foundations of Machine Learning |date=2012 |publisher=The MIT Press |isbn=9780262018258}}</ref> An optimal function allows the algorithm to correctly determine the output for inputs that were not a part of the training data. An algorithm that improves the accuracy of its outputs or predictions over time is said to have learned to perform that task.<ref name="Mitchell-1997" />

Types of supervised-learning algorithms include [[Active learning (machine learning)|active learning]], [[Statistical classification|classification]] and [[Regression analysis|regression]].<ref name=":3">{{cite book|last=Alpaydin|first=Ethem|title=Introduction to Machine Learning|date=2010|publisher=MIT Press|isbn=978-0-262-01243-0|page=9|url=https://books.google.com/books?id=7f5bBAAAQBAJ|access-date=2018-11-25|archive-date=2023-01-17|archive-url=https://web.archive.org/web/20230117053338/https://books.google.com/books?id=7f5bBAAAQBAJ|url-status=live}}</ref> Classification algorithms are used when the outputs are restricted to a limited set of values, and regression algorithms are used when the outputs may have any numerical value within a range. As an example, for a classification algorithm that filters emails, the input would be an incoming email, and the output would be the name of the folder in which to file the email.

[[Similarity learning]] is an area of supervised machine learning closely related to regression and classification, but the goal is to learn from examples using a similarity function that measures how similar or related two objects are. It has applications in [[Ranking|ranking]], [[Recommender system|recommendation systems]], visual identity tracking, face verification, and speaker verification.

=== Unsupervised learning ===
Unsupervised learning algorithms find structures in data that has not been labeled, classified or categorized. Instead of responding to feedback, unsupervised learning algorithms identify commonalities in the data and react based on the presence or absence of such commonalities in each new piece of data. Central applications of unsupervised machine learning include clustering, [[Dimensionality reduction|dimensionality reduction]],<ref name=":9" /> and [[Density estimation|density estimation]].<ref name="JordanBishop2004">{{cite book |first1=Michael I. |last1=Jordan |first2=Christopher M. |last2=Bishop |chapter=Neural Networks |editor=Allen B. Tucker |title=Computer Science Handbook, Second Edition (Section VII: Intelligent Systems) |location=Boca Raton, Florida |publisher=Chapman & Hall/CRC Press LLC |year=2004 |isbn=978-1-58488-360-9 }}</ref> Unsupervised learning algorithms also streamlined the process of identifying large [[Biology:Indel|indel]] based [[Biology:Haplotype|haplotype]]s of a gene of interest from [[Biology:Pan-genome|pan-genome]].<ref>{{Cite journal |last1=Zhang |first1=Bosen |last2=Huang |first2=Haiyan |last3=Tibbs-Cortes |first3=Laura E. |last4=Vanous |first4=Adam |last5=Zhang |first5=Zhiwu |last6=Sanguinet |first6=Karen |last7=Garland-Campbell |first7=Kimberly A. |last8=Yu |first8=Jianming |last9=Li |first9=Xianran |title=Streamline unsupervised machine learning to survey and graph indel-based haplotypes from pan-genomes |journal=Molecular Plant |year=2023 |volume=16 |issue=6 |pages=975–978 |language=en |doi=10.1016/j.molp.2023.05.005|pmid=37202927 |doi-access=free }}</ref>  
[[File:CLIPS.jpg|thumb|542x542px|Clustering via Large Indel Permuted Slopes, CLIPS, turns the alignment image into a learning regression problem. The varied slope (''b'') estimates between each pair of DNA segments enables to identify segments sharing the same set of indels.]]

Cluster analysis is the assignment of a set of observations into subsets (called ''clusters'') so that observations within the same cluster are similar according to one or more predesignated criteria, while observations drawn from different clusters are dissimilar. Different clustering techniques make different assumptions on the structure of the data, often defined by some ''similarity metric'' and evaluated, for example, by ''internal compactness'', or the similarity between members of the same cluster, and ''separation'', the difference between clusters. Other methods are based on ''estimated density'' and ''graph connectivity''.

=== Semi-supervised learning ===
{{Main|Semi-supervised learning}}

Semi-supervised learning falls between [[Unsupervised learning|unsupervised learning]] (without any labeled training data) and [[Supervised learning|supervised learning]] (with completely labeled training data). Some of the training examples are missing training labels, yet many machine-learning researchers have found that unlabeled data, when used in conjunction with a small amount of labeled data, can produce a considerable improvement in learning accuracy.

In [[Weak supervision|weakly supervised learning]], the training labels are noisy, limited, or imprecise; however, these labels are often cheaper to obtain, resulting in larger effective training sets.<ref>{{Cite web|url=https://hazyresearch.github.io/snorkel/blog/ws_blog_post.html|title=Weak Supervision: The New Programming Paradigm for Machine Learning|author1=Alex Ratner|author2=Stephen Bach|author3=Paroma Varma|author4=Chris|others=referencing work by many other members of Hazy Research|website=hazyresearch.github.io|access-date=2019-06-06|archive-date=2019-06-06|archive-url=https://web.archive.org/web/20190606043931/https://hazyresearch.github.io/snorkel/blog/ws_blog_post.html}}</ref>

=== Reinforcement learning ===
{{Main|Reinforcement learning}}
Reinforcement learning is an area of machine learning concerned with how [[Software agent|software agent]]s ought to take [[Action selection|actions]] in an environment so as to maximize some notion of cumulative reward. Due to its generality, the field is studied in many other disciplines, such as [[Game theory|game theory]], [[Control theory|control theory]], [[Operations research|operations research]], [[Information theory|information theory]], [[Simulation-based optimization|simulation-based optimization]], [[Multi-agent system|multi-agent system]]s, [[Swarm intelligence|swarm intelligence]], [[Statistics|statistics]] and [[Genetic algorithm|genetic algorithm]]s. In reinforcement learning, the environment is typically represented as a [[Markov decision process]] (MDP). Many reinforcements learning algorithms use [[Dynamic programming|dynamic programming]] techniques.<ref>{{Cite book|author1=van Otterlo, M.|author2=Wiering, M.|title=Reinforcement Learning |chapter=Reinforcement Learning and Markov Decision Processes |volume=12|pages=3–42 |year=2012 |doi=10.1007/978-3-642-27645-3_1|series=Adaptation, Learning, and Optimization|isbn=978-3-642-27644-6}}</ref> Reinforcement learning algorithms do not assume knowledge of an exact mathematical model of the MDP and are used when exact models are infeasible. Reinforcement learning algorithms are used in autonomous vehicles or in learning to play a game against a human opponent.

=== Dimensionality reduction ===
[[Dimensionality reduction]] is a process of reducing the number of random variables under consideration by obtaining a set of principal variables.<ref>{{cite journal|url=https://science.sciencemag.org/content/290/5500/2323|title=Nonlinear Dimensionality Reduction by Locally Linear Embedding|first1=Sam T.|last1=Roweis|first2=Lawrence K.|last2=Saul|date=22 Dec 2000|journal=Science|volume=290|issue=5500|pages=2323–2326|doi=10.1126/science.290.5500.2323|pmid=11125150 |bibcode=2000Sci...290.2323R |s2cid=5987139 |language=en}}</ref> In other words, it is a process of reducing the dimension of the [[Feature (machine learning)|feature]] set, also called the "number of features". Most of the dimensionality reduction techniques can be considered as either feature elimination or [[Feature extraction|extraction]]. One of the popular methods of dimensionality reduction is [[Principal component analysis|principal component analysis]] (PCA). PCA involves changing higher-dimensional data (e.g., 3D) to a smaller space (e.g., 2D). This results in a smaller dimension of data (2D instead of 3D), while keeping all original variables in the model without changing the data.<ref>{{cite web|url=https://towardsdatascience.com/all-machine-learning-models-explained-in-6-minutes-9fe30ff6776a|title=All Machine Learning Models Explained in 6 Minutes. Intuitive explanations of the most popular machine learning models|first=Terence|last=Shin|date=Jan 5, 2020|website=Towards Data Science|language=en}}</ref>
The [[Manifold hypothesis|manifold hypothesis]] proposes that high-dimensional data sets lie along low-dimensional [[Manifold|manifold]]s, and many dimensionality reduction techniques make this assumption, leading to the area of manifold learning and [[Manifold regularization|manifold regularization]].

=== Other types ===
Other approaches have been developed which do not fit neatly into this three-fold categorization, and sometimes more than one is used by the same machine learning system. For example, topic modeling, [[Meta-learning (computer science)|meta-learning]].<ref>{{cite book
 |author=Pavel Brazdil |author2=Christophe Giraud Carrier |author3=Carlos Soares |author4=Ricardo Vilalta
 | title =Metalearning: Applications to Data Mining
 | year = 2009
 | edition = Fourth
 | pages = 10–14, ''passim''
 | publisher = [[Company:Springer Science+Business Media|Springer Science+Business Media]]
 |isbn = 978-3540732624
 }}</ref>

==== Self-learning ====
Self-learning, as a machine learning paradigm was introduced in 1982 along with a neural network capable of self-learning, named ''crossbar adaptive array'' (CAA).<ref>Bozinovski, S. (1982). "A self-learning system using secondary reinforcement". In Trappl, Robert (ed.). Cybernetics and Systems Research: Proceedings of the Sixth European Meeting on Cybernetics and Systems Research. North-Holland. pp. 397–402. {{ISBN|978-0-444-86488-8}}.</ref> It is learning with no external rewards and no external teacher advice. The CAA self-learning algorithm computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about consequence situations. The system is driven by the interaction between cognition and emotion.<ref>Bozinovski, Stevo (2014) "Modeling mechanisms of cognition-emotion interaction in artificial neural networks, since 1981." Procedia Computer Science p. 255-263</ref>
The self-learning algorithm updates a memory matrix W =||w(a,s)|| such that in each iteration executes the following machine learning routine: 
#  in situation ''s'' perform action ''a''
#  receive a consequence situation ''s'''
#  compute emotion of being in the consequence situation ''v(s')''
#  update crossbar memory  ''w'(a,s) = w(a,s) + v(s')''

It is a system with only one input, situation, and only one output, action (or behavior) a. There is neither a separate reinforcement input nor an advice input from the environment. The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is the behavioral environment where it behaves, and the other is the genetic environment, wherefrom it initially and only once receives initial emotions about situations to be encountered in the behavioral environment. After receiving the genome (species) vector from the genetic environment, the CAA learns a goal-seeking behavior, in an environment that contains both desirable and undesirable situations.<ref>Bozinovski, S. (2001) "Self-learning agents: A connectionist theory of emotion based on crossbar value judgment." Cybernetics and Systems 32(6) 637–667.</ref>

==== Feature learning ====
{{Main|Feature learning}}

Several learning algorithms aim at discovering better representations of the inputs provided during training.<ref name="pami">{{cite journal |author1=Y. Bengio |author2=A. Courville |author3=P. Vincent |title=Representation Learning: A Review and New Perspectives |journal= IEEE Transactions on Pattern Analysis and Machine Intelligence|year=2013|doi=10.1109/tpami.2013.50 |pmid=23787338 |volume=35 |issue=8 |pages=1798–1828|arxiv=1206.5538 |s2cid=393948 }}</ref> Classic examples include [[Principal component analysis|principal component analysis]] and cluster analysis. Feature learning algorithms, also called representation learning algorithms, often attempt to preserve the information in their input but also transform it in a way that makes it useful, often as a pre-processing step before performing classification or predictions. This technique allows reconstruction of the inputs coming from the unknown data-generating distribution, while not being necessarily faithful to configurations that are implausible under that distribution. This replaces manual [[Feature engineering|feature engineering]], and allows a machine to both learn the features and use them to perform a specific task.

Feature learning can be either supervised or unsupervised. In supervised feature learning, features are learned using labeled input data. Examples include [[Artificial neural network|artificial neural network]]s, [[Multilayer perceptron|multilayer perceptron]]s, and supervised dictionary learning. In unsupervised feature learning, features are learned with unlabeled input data.  Examples include dictionary learning, [[Independent component analysis|independent component analysis]], [[Autoencoder|autoencoder]]s, [[Matrix decomposition|matrix factorization]]<ref>{{cite conference |author1=Nathan Srebro |author2=Jason D. M. Rennie |author3=Tommi S. Jaakkola |title=Maximum-Margin Matrix Factorization |conference=[[Conference on Neural Information Processing Systems|NIPS]] |year=2004}}</ref> and various forms of [[Cluster analysis|clustering]].<ref name="coates2011">{{cite conference
|last1 = Coates
|first1 = Adam
|last2 = Lee
|first2 = Honglak
|last3 = Ng
|first3 = Andrew Y.
|title = An analysis of single-layer networks in unsupervised feature learning
|conference = Int'l Conf. on AI and Statistics (AISTATS)
|year = 2011
|url = http://machinelearning.wustl.edu/mlpapers/paper_files/AISTATS2011_CoatesNL11.pdf
|access-date = 2018-11-25
|archive-url = https://web.archive.org/web/20170813153615/http://machinelearning.wustl.edu/mlpapers/paper_files/AISTATS2011_CoatesNL11.pdf
|archive-date = 2017-08-13
}}</ref><ref>{{cite conference|last1 = Csurka|first1 = Gabriella|last2 = Dance|first2 = Christopher C.|last3 = Fan|first3 = Lixin|last4 = Willamowski|first4 = Jutta|last5 = Bray|first5 = Cédric|title = Visual categorization with bags of keypoints|conference = ECCV Workshop on Statistical Learning in Computer Vision|year = 2004|url = https://www.cs.cmu.edu/~efros/courses/LBMV07/Papers/csurka-eccv-04.pdf|access-date = 2019-08-29|archive-date = 2019-07-13|archive-url = https://web.archive.org/web/20190713040210/http://www.cs.cmu.edu/~efros/courses/LBMV07/Papers/csurka-eccv-04.pdf|url-status = live}}</ref><ref name="jurafsky">{{cite book |title=Speech and Language Processing |author1=Daniel Jurafsky |author2=James H. Martin |publisher=Pearson Education International |year=2009 |pages=145–146}}</ref>

Manifold learning algorithms attempt to do so under the constraint that the learned representation is low-dimensional. Sparse coding algorithms attempt to do so under the constraint that the learned representation is sparse, meaning that the mathematical model has many zeros. [[Multilinear subspace learning]] algorithms aim to learn low-dimensional representations directly from [[Tensor|tensor]] representations for multidimensional data, without reshaping them into higher-dimensional vectors.<ref>{{cite journal |first1=Haiping |last1=Lu |first2=K.N. |last2=Plataniotis |first3=A.N. |last3=Venetsanopoulos |url=http://www.dsp.utoronto.ca/~haiping/Publication/SurveyMSL_PR2011.pdf |title=A Survey of Multilinear Subspace Learning for Tensor Data |journal=Pattern Recognition |volume=44 |number=7 |pages=1540–1551 |year=2011 |doi=10.1016/j.patcog.2011.01.004 |bibcode=2011PatRe..44.1540L |access-date=2015-09-04 |archive-date=2019-07-10 |archive-url=https://web.archive.org/web/20190710225429/http://www.dsp.utoronto.ca/~haiping/Publication/SurveyMSL_PR2011.pdf |url-status=live }}</ref> [[Deep learning]] algorithms discover multiple levels of representation, or a hierarchy of features, with higher-level, more abstract features defined in terms of (or generating) lower-level features. It has been argued that an intelligent machine is one that learns a representation that disentangles the underlying factors of variation that explain the observed data.<ref>{{cite book | title = Learning Deep Architectures for AI | author = Yoshua Bengio | publisher = Now Publishers Inc. | year = 2009 | isbn = 978-1-60198-294-0 | pages = 1–3 | url = https://books.google.com/books?id=cq5ewg7FniMC&pg=PA3 |  access-date = 2016-02-15 | archive-date = 2023-01-17 | archive-url = https://web.archive.org/web/20230117053339/https://books.google.com/books?id=cq5ewg7FniMC&pg=PA3 | url-status = live }}</ref>

Feature learning is motivated by the fact that machine learning tasks such as classification often require input that is mathematically and computationally convenient to process. However, real-world data such as images, video, and sensory data has not yielded attempts to algorithmically define specific features. An alternative is to discover such features or representations through examination, without relying on explicit algorithms.

==== Sparse dictionary learning ====
{{Main|Sparse dictionary learning}}
Sparse dictionary learning is a feature learning method where a training example is represented as a linear combination of [[Basis function|basis function]]s, and is assumed to be a [[Sparse matrix|sparse matrix]]. The method is strongly NP-hard and difficult to solve approximately.<ref>{{cite journal |first=A. M. |last=Tillmann |title=On the Computational Intractability of Exact and Approximate Dictionary Learning |journal=IEEE Signal Processing Letters |volume=22 |issue=1 |year=2015 |pages=45–49 |doi=10.1109/LSP.2014.2345761|bibcode=2015ISPL...22...45T |arxiv=1405.6664 |s2cid=13342762 }}</ref> A popular [[Heuristic|heuristic]] method for sparse dictionary learning is the [[K-SVD]] algorithm. Sparse dictionary learning has been applied in several contexts. In classification, the problem is to determine the class to which a previously unseen training example belongs. For a dictionary where each class has already been built, a new training example is associated with the class that is best sparsely represented by the corresponding dictionary. Sparse dictionary learning has also been applied in image de-noising. The key idea is that a clean image patch can be sparsely represented by an image dictionary, but the noise cannot.<ref>Aharon, M, M Elad, and A Bruckstein. 2006. "[http://sites.fas.harvard.edu/~cs278/papers/ksvd.pdf K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation] {{Webarchive|url=https://web.archive.org/web/20181123142158/http://sites.fas.harvard.edu/~cs278/papers/ksvd.pdf |date=2018-11-23 }}." Signal Processing, IEEE Transactions on 54 (11): 4311–4322</ref>

==== Anomaly detection ====
{{Main|Anomaly detection}}
In [[Data mining|data mining]], anomaly detection, also known as outlier detection, is the identification of rare items, events or observations which raise suspicions by differing significantly from the majority of the data.<ref name=":0">{{Citation|last1=Zimek|first1=Arthur|title=Outlier Detection|date=2017|encyclopedia=Encyclopedia of Database Systems|pages=1–5|publisher=Springer New York|language=en|doi=10.1007/978-1-4899-7993-3_80719-1|isbn=9781489979933|last2=Schubert|first2=Erich}}</ref> Typically, the anomalous items represent an issue such as [[Finance:Bank fraud|bank fraud]], a structural defect, medical problems or errors in a text. Anomalies are referred to as [[Outlier|outlier]]s, novelties, noise, deviations and exceptions.<ref>{{cite journal | last1 = Hodge | first1 = V. J. | last2 = Austin | first2 = J. | doi = 10.1007/s10462-004-4304-y | title = A Survey of Outlier Detection Methodologies | journal = Artificial Intelligence Review | volume = 22 | issue = 2 | pages = 85–126 | year = 2004 | url = http://eprints.whiterose.ac.uk/767/1/hodgevj4.pdf | citeseerx = 10.1.1.318.4023 | s2cid = 59941878 | access-date = 2018-11-25 | archive-date = 2015-06-22 | archive-url = https://web.archive.org/web/20150622042146/http://eprints.whiterose.ac.uk/767/1/hodgevj4.pdf | url-status = live }}</ref>

In particular, in the context of abuse and network intrusion detection, the interesting objects are often not rare objects, but unexpected bursts of inactivity. This pattern does not adhere to the common statistical definition of an outlier as a rare object. Many outlier detection methods (in particular, unsupervised algorithms) will fail on such data unless aggregated appropriately. Instead, a cluster analysis algorithm may be able to detect the micro-clusters formed by these patterns.<ref>{{cite journal |first1=Paul |last1=Dokas |first2=Levent |last2=Ertoz |first3=Vipin |last3=Kumar |first4=Aleksandar |last4=Lazarevic |first5=Jaideep |last5=Srivastava |first6=Pang-Ning |last6=Tan |title=Data mining for network intrusion detection |year=2002 |journal=Proceedings NSF Workshop on Next Generation Data Mining |url=https://www-users.cse.umn.edu/~lazar027/MINDS/papers/nsf_ngdm_2002.pdf |access-date=2023-03-26 |archive-date=2015-09-23 |archive-url=https://web.archive.org/web/20150923211542/http://www.csee.umbc.edu/~kolari1/Mining/ngdm/dokas.pdf |url-status=live }}</ref>

Three broad categories of anomaly detection techniques exist.<ref name="ChandolaSurvey">{{cite journal |last1=Chandola |first1=V. |last2=Banerjee |first2=A. |last3=Kumar |first3=V. |s2cid=207172599 |year=2009 |title=Anomaly detection: A survey|journal=[[ACM Computing Surveys]]|volume=41|issue=3|pages=1–58|doi=10.1145/1541880.1541882}}</ref> Unsupervised anomaly detection techniques detect anomalies in an unlabeled test data set under the assumption that the majority of the instances in the data set are normal, by looking for instances that seem to fit the least to the remainder of the data set. Supervised anomaly detection techniques require a data set that has been labeled as "normal" and "abnormal" and involves training a classifier (the key difference to many other statistical classification problems is the inherently unbalanced nature of outlier detection). Semi-supervised anomaly detection techniques construct a model representing normal behavior from a given normal training data set and then test the likelihood of a test instance to be generated by the model.

==== Robot learning ====
[[Robot learning]] is inspired by a multitude of machine learning methods, starting from supervised learning, reinforcement learning,<ref>{{cite journal|title=Learning efficient haptic shape exploration with a rigid tactile sensor array, S. Fleer, A. Moringen, R. Klatzky, H. Ritter |year=2020 |doi=10.1371/journal.pone.0226880|arxiv=1902.07501 |pmid=31896135 |doi-access=free |last1=Fleer |first1=S. |last2=Moringen |first2=A. |last3=Klatzky |first3=R. L. |last4=Ritter |first4=H. |journal=PLOS ONE |volume=15 |issue=1 |pages=e0226880 |pmc=6940144 }}</ref><ref>{{Citation|last1=Moringen|first1=Alexandra|title=Attention-Based Robot Learning of Haptic Interaction|date=2020|work=Haptics: Science, Technology, Applications|volume=12272|pages=462–470|editor-last=Nisky|editor-first=Ilana|place=Cham|publisher=Springer International Publishing|language=en|doi=10.1007/978-3-030-58147-3_51|isbn=978-3-030-58146-6|last2=Fleer|first2=Sascha|last3=Walck|first3=Guillaume|last4=Ritter|first4=Helge|series=Lecture Notes in Computer Science |s2cid=220069113|editor2-last=Hartcher-O'Brien|editor2-first=Jess|editor3-last=Wiertlewski|editor3-first=Michaël|editor4-last=Smeets|editor4-first=Jeroen|doi-access=free}}</ref> and finally [[Meta-learning (computer science)|meta-learning]] (e.g. MAML).

==== Association rules ====
Association rule learning is a [[Rule-based machine learning|rule-based machine learning]] method for discovering relationships between variables in large databases. It is intended to identify strong rules discovered in databases using some measure of "interestingness".<ref name="piatetsky">Piatetsky-Shapiro, Gregory (1991), ''Discovery, analysis, and presentation of strong rules'', in Piatetsky-Shapiro, Gregory; and Frawley, William J.; eds., ''Knowledge Discovery in Databases'', AAAI/MIT Press, Cambridge, MA.</ref>

Rule-based machine learning is a general term for any machine learning method that identifies, learns, or evolves "rules" to store, manipulate or apply knowledge. The defining characteristic of a rule-based machine learning algorithm is the identification and utilization of a set of relational rules that collectively represent the knowledge captured by the system. This is in contrast to other machine learning algorithms that commonly identify a singular model that can be universally applied to any instance in order to make a prediction.<ref>{{Cite journal|last1=Bassel|first1=George W.|last2=Glaab|first2=Enrico|last3=Marquez|first3=Julietta|last4=Holdsworth|first4=Michael J.|last5=Bacardit|first5=Jaume|date=2011-09-01|title=Functional Network Construction in Arabidopsis Using Rule-Based Machine Learning on Large-Scale Data Sets|journal=The Plant Cell|language=en|volume=23|issue=9|pages=3101–3116|doi=10.1105/tpc.111.088153|issn=1532-298X|pmc=3203449|pmid=21896882}}</ref> Rule-based machine learning approaches include [[Learning classifier system|learning classifier system]]s, association rule learning, and [[Artificial immune system|artificial immune system]]s.

Based on the concept of strong rules, Rakesh Agrawal, Tomasz Imieliński and Arun Swami introduced association rules for discovering regularities between products in large-scale transaction data recorded by point-of-sale (POS) systems in supermarkets.<ref name="mining">{{Cite book | last1 = Agrawal | first1 = R. | last2 = Imieliński | first2 = T. | last3 = Swami | first3 = A. | doi = 10.1145/170035.170072 | chapter = Mining association rules between sets of items in large databases | title = Proceedings of the 1993 ACM SIGMOD international conference on Management of data - SIGMOD '93 | pages = 207 | year = 1993 | isbn = 978-0897915922 | citeseerx = 10.1.1.40.6984 | s2cid = 490415 }}</ref> For example, the rule <math>\{\mathrm{onions, potatoes}\} \Rightarrow \{\mathrm{burger}\}</math> found in the sales data of a supermarket would indicate that if a customer buys onions and potatoes together, they are likely to also buy hamburger meat. Such information can be used as the basis for decisions about marketing activities such as promotional [[Finance:Pricing|pricing]] or [[Finance:Product placement|product placement]]s. In addition to market basket analysis, association rules are employed today in application areas including Web usage mining, intrusion detection, continuous production, and [[Biology:Bioinformatics|bioinformatics]]. In contrast with sequence mining, association rule learning typically does not consider the order of items either within a transaction or across transactions.

Learning classifier systems (LCS) are a family of rule-based machine learning algorithms that combine a discovery component, typically a [[Genetic algorithm|genetic algorithm]], with a learning component, performing either [[Supervised learning|supervised learning]], [[Reinforcement learning|reinforcement learning]], or [[Unsupervised learning|unsupervised learning]]. They seek to identify a set of context-dependent rules that collectively store and apply knowledge in a [[Piecewise|piecewise]] manner in order to make predictions.<ref>{{Cite journal|last1=Urbanowicz|first1=Ryan J.|last2=Moore|first2=Jason H.|date=2009-09-22|title=Learning Classifier Systems: A Complete Introduction, Review, and Roadmap|journal=Journal of Artificial Evolution and Applications|language=en|volume=2009|pages=1–25|doi=10.1155/2009/736398|issn=1687-6229|doi-access=free}}</ref>

[[Inductive logic programming]] (ILP) is an approach to rule learning using [[Logic programming|logic programming]] as a uniform representation for input examples, background knowledge, and hypotheses. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesized logic program that entails all positive and no negative examples. [[Inductive programming]] is a related field that considers any kind of programming language for representing hypotheses (and not only logic programming), such as [[Functional programming|functional programs]].

Inductive logic programming is particularly useful in [[Biology:Bioinformatics|bioinformatics]] and [[Natural language processing|natural language processing]]. [[Biography:Gordon Plotkin|Gordon Plotkin]] and [[Biography:Ehud Shapiro|Ehud Shapiro]] laid the initial theoretical foundation for inductive machine learning in a logical setting.<ref>Plotkin G.D. [https://www.era.lib.ed.ac.uk/bitstream/handle/1842/6656/Plotkin1972.pdf;sequence=1 Automatic Methods of Inductive Inference] {{Webarchive|url=https://web.archive.org/web/20171222051034/https://www.era.lib.ed.ac.uk/bitstream/handle/1842/6656/Plotkin1972.pdf;sequence=1 |date=2017-12-22 }}, PhD thesis, University of Edinburgh, 1970.</ref><ref>Shapiro, Ehud Y. [http://ftp.cs.yale.edu/publications/techreports/tr192.pdf Inductive inference of theories from facts] {{Webarchive|url=https://web.archive.org/web/20210821071609/http://ftp.cs.yale.edu/publications/techreports/tr192.pdf |date=2021-08-21 }}, Research Report 192, Yale University, Department of Computer Science, 1981. Reprinted in J.-L. Lassez, G. Plotkin (Eds.), Computational Logic, The MIT Press, Cambridge, MA, 1991, pp. 199–254.</ref><ref>Shapiro, Ehud Y. (1983). ''Algorithmic program debugging''. Cambridge, Mass: MIT Press. {{ISBN|0-262-19218-7}}</ref> Shapiro built their first implementation (Model Inference System) in 1981: a Prolog program that inductively inferred logic programs from positive and negative examples.<ref>Shapiro, Ehud Y. "[http://dl.acm.org/citation.cfm?id=1623364 The model inference system]." Proceedings of the 7th international joint conference on Artificial intelligence-Volume 2. Morgan Kaufmann Publishers Inc., 1981.</ref> The term ''inductive'' here refers to [[Philosophy:Inductive reasoning|philosophical]] induction, suggesting a theory to explain observed facts, rather than [[Mathematical induction|mathematical induction]], proving a property for all members of a well-ordered set.

=== Models ===
Performing machine learning can involve creating a [[Statistical model|model]], which is trained on some training data and then can process additional data to make predictions. Various types of models have been used and researched for machine learning systems.

==== Artificial neural networks ====
[[File:Colored neural network.svg|thumb|300px|An artificial neural network is an interconnected group of nodes, akin to the vast network of neurons in a brain. Here, each circular node represents an [[Artificial neuron|artificial neuron]] and an arrow represents a connection from the output of one artificial neuron to the input of another.]]

Artificial neural networks (ANNs), or [[Connectionism|connectionist]] systems, are computing systems vaguely inspired by the biological neural networks that constitute animal [[Biology:Brain|brain]]s. Such systems "learn" to perform tasks by considering examples, generally without being programmed with any task-specific rules.

An ANN is a model based on a collection of connected units or nodes called "[[Artificial neuron|artificial neuron]]s", which loosely model the [[Biology:Neuron|neuron]]s in a biological [[Biology:Brain|brain]]. Each connection, like the [[Biology:Synapse|synapse]]s in a biological [[Biology:Brain|brain]], can transmit information, a "signal", from one artificial neuron to another. An artificial neuron that receives a signal can process it and then signal additional artificial neurons connected to it. In common ANN implementations, the signal at a connection between artificial neurons is a [[Real number|real number]], and the output of each artificial neuron is computed by some non-linear function of the sum of its inputs. The connections between artificial neurons are called "edges". Artificial neurons and edges typically have a weight that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Artificial neurons may have a threshold such that the signal is only sent if the aggregate signal crosses that threshold. Typically, artificial neurons are aggregated into layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first layer (the input layer) to the last layer (the output layer), possibly after traversing the layers multiple times.

The original goal of the ANN approach was to solve problems in the same way that a [[Biology:Human brain|human brain]] would. However, over time, attention moved to performing specific tasks, leading to deviations from [[Biology:Biology|biology]]. Artificial neural networks have been used on a variety of tasks, including [[Computer vision|computer vision]], [[Speech recognition|speech recognition]], [[Machine translation|machine translation]], [[Social:Social network|social network]] filtering, [[General game playing|playing board and video games]] and [[Medicine:Medical diagnosis|medical diagnosis]].

[[Deep learning]] consists of multiple hidden layers in an artificial neural network. This approach tries to model the way the human brain processes light and sound into vision and hearing. Some successful applications of deep learning are [[Computer vision|computer vision]] and [[Speech recognition|speech recognition]].<ref>Honglak Lee, Roger Grosse, Rajesh Ranganath, Andrew Y. Ng. "[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.149.802&rep=rep1&type=pdf Convolutional Deep Belief Networks for Scalable Unsupervised Learning of Hierarchical Representations] {{Webarchive|url=https://web.archive.org/web/20171018182235/http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.149.802&rep=rep1&type=pdf |date=2017-10-18 }}" Proceedings of the 26th Annual International Conference on Machine Learning, 2009.</ref>

==== Decision trees ====
{{Main|Decision tree learning}}
[[File:Decision Tree.jpg|thumb|A decision tree showing survival probability of passengers on the Titanic]]

Decision tree learning uses a [[Decision tree|decision tree]] as a predictive model to go from observations about an item (represented in the branches) to conclusions about the item's target value (represented in the leaves). It is one of the predictive modeling approaches used in statistics, data mining, and machine learning. Tree models where the target variable can take a discrete set of values are called classification trees; in these tree structures, [[Leaf node|leaves]] represent class labels, and branches represent [[Logical conjunction|conjunction]]s of features that lead to those class labels. Decision trees where the target variable can take continuous values (typically real numbers) are called regression trees. In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining, a decision tree describes data, but the resulting classification tree can be an input for decision-making.

==== Support-vector machines ====
{{Main|Support-vector machine}}
Support-vector machines (SVMs), also known as support-vector networks, are a set of related [[Supervised learning|supervised learning]] methods used for classification and regression. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category.<ref name="CorinnaCortes">{{Cite journal |last1=Cortes |first1=Corinna |last2=Vapnik |first2=Vladimir N. |year=1995 |title=Support-vector networks |journal=Machine Learning |volume=20 |issue=3 |pages=273–297 |doi=10.1007/BF00994018 |doi-access=free }}</ref>  An SVM training algorithm is a non-[[Probabilistic classification|probabilistic]], binary, [[Linear classifier|linear classifier]], although methods such as [[Platt scaling]] exist to use SVM in a probabilistic classification setting. In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces.

==== Regression analysis ====
{{Main|Regression analysis}}
[[Image:Linear regression.svg|thumb|upright=1.3|Illustration of linear regression on a data set]]

Regression analysis encompasses a large variety of statistical methods to estimate the relationship between input variables and their associated features. Its most common form is [[Linear regression|linear regression]], where a single line is drawn to best fit the given data according to a mathematical criterion such as [[Ordinary least squares|ordinary least squares]]. The latter is often extended by [[Regularization (mathematics)|regularization]] methods to mitigate overfitting and bias, as in [[Ridge regression|ridge regression]]. When dealing with non-linear problems, go-to models include [[Polynomial regression|polynomial regression]] (for example, used for trendline fitting in Microsoft Excel<ref>{{cite web|last1=Stevenson|first1=Christopher|title=Tutorial: Polynomial Regression in Excel|url=https://facultystaff.richmond.edu/~cstevens/301/Excel4.html|website=facultystaff.richmond.edu|access-date=22 January 2017|archive-date=2 June 2013|archive-url=https://web.archive.org/web/20130602200850/https://facultystaff.richmond.edu/~cstevens/301/Excel4.html|url-status=live}}</ref>), [[Logistic regression|logistic regression]] (often used in [[Statistical classification|statistical classification]]) or even [[Kernel regression|kernel regression]], which introduces non-linearity by taking advantage of the kernel trick to implicitly map input variables to higher-dimensional space.

==== Bayesian networks ====
{{Main|Bayesian network}}
[[Image:SimpleBayesNetNodes.svg|thumb|right|A simple Bayesian network. Rain influences whether the sprinkler is activated, and both rain and the sprinkler influence whether the grass is wet.]]

A Bayesian network, belief network, or directed acyclic graphical model is a probabilistic [[Graphical model|graphical model]] that represents a set of random variables and their [[Conditional independence|conditional independence]] with a [[Directed acyclic graph|directed acyclic graph]] (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms exist that perform [[Bayesian inference|inference]] and learning. Bayesian networks that model sequences of variables, like [[Speech recognition|speech signals]] or [[Biology:Peptide sequence|protein sequences]], are called [[Dynamic Bayesian network|dynamic Bayesian network]]s. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called [[Influence diagram|influence diagram]]s.

==== Gaussian processes ====
[[Image:Regressions sine demo.svg|thumbnail|right|An example of Gaussian Process Regression (prediction) compared with other regression models<ref>The documentation for scikit-learn also has similar [http://scikit-learn.org/stable/auto_examples/gaussian_process/plot_compare_gpr_krr.html examples] {{Webarchive|url=https://web.archive.org/web/20221102184805/https://scikit-learn.org/stable/auto_examples/gaussian_process/plot_compare_gpr_krr.html |date=2022-11-02 }}.</ref>]]

A Gaussian process is a [[Stochastic process|stochastic process]] in which every finite collection of the random variables in the process has a [[Multivariate normal distribution|multivariate normal distribution]], and it relies on a pre-defined [[Covariance function|covariance function]], or kernel, that models how pairs of points relate to each other depending on their locations.

Given a set of observed points, or input–output examples, the distribution of the (unobserved) output of a new point as function of its input data can be directly computed by looking like the observed points and the covariances between those points and the new, unobserved point.

Gaussian processes are popular surrogate models in [[Bayesian optimization]] used to do [[Hyperparameter optimization|hyperparameter optimization]].

==== Genetic algorithms ====
{{Main|Genetic algorithm}}
A genetic algorithm (GA) is a [[Search algorithm|search algorithm]] and [[Heuristic (computer science)|heuristic]] technique that mimics the process of [[Biology:Natural selection|natural selection]], using methods such as [[Mutation (genetic algorithm)|mutation]] and [[Crossover (genetic algorithm)|crossover]] to generate new [[Chromosome (genetic algorithm)|genotype]]s in the hope of finding good solutions to a given problem. In machine learning, genetic algorithms were used in the 1980s and 1990s.<ref>{{cite journal |last1=Goldberg |first1=David E. |first2=John H. |last2=Holland |title=Genetic algorithms and machine learning |journal=Machine Learning |volume=3 |issue=2 |year=1988 |pages=95–99 |doi=10.1007/bf00113892 |s2cid=35506513 |url=https://deepblue.lib.umich.edu/bitstream/2027.42/46947/1/10994_2005_Article_422926.pdf |doi-access=free |access-date=2019-09-03 |archive-date=2011-05-16 |archive-url=https://web.archive.org/web/20110516025803/http://deepblue.lib.umich.edu/bitstream/2027.42/46947/1/10994_2005_Article_422926.pdf |url-status=live }}</ref><ref>{{Cite journal |title=Machine Learning, Neural and Statistical Classification |journal=Ellis Horwood Series in Artificial Intelligence |first1=D. |last1=Michie |first2=D. J. |last2=Spiegelhalter |first3=C. C. |last3=Taylor |year=1994 |bibcode=1994mlns.book.....M }}</ref> Conversely, machine learning techniques have been used to improve the performance of genetic and [[Evolutionary algorithm|evolutionary algorithm]]s.<ref>{{cite journal |last1=Zhang |first1=Jun |last2=Zhan |first2=Zhi-hui |last3=Lin |first3=Ying |last4=Chen |first4=Ni |last5=Gong |first5=Yue-jiao |last6=Zhong |first6=Jing-hui |last7=Chung |first7=Henry S.H. |last8=Li |first8=Yun |last9=Shi |first9=Yu-hui |title=Evolutionary Computation Meets Machine Learning: A Survey |journal=Computational Intelligence Magazine |year=2011 |volume=6 |issue=4 |pages=68–75 |doi=10.1109/mci.2011.942584|s2cid=6760276 }}</ref>

====Belief functions====
{{Main|Philosophy:Dempster–Shafer theory}}
The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory, is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as [[Probability|probability]], [[Possibility theory|possibility]] and  [[Imprecise probability|imprecise probability theories]]. These theoretical frameworks can be thought of as a kind of learner and have some analogous properties of how evidence is combined (e.g.,  Dempster's rule of combination), just like how in a [[Probability mass function|pmf]]-based Bayesian approach{{clarify|date=January 2024}} would combine probabilities. However, there are many caveats to these beliefs functions when compared to Bayesian approaches in order to incorporate ignorance and [[Uncertainty quantification]]. These belief function approaches that are implemented within the machine learning domain typically leverage a fusion approach of various ensemble methods to better handle the learner's [[Decision boundary|decision boundary]], low samples, and ambiguous class issues that standard machine learning approach tend to have difficulty resolving.<ref name=":6" /><ref name=":7" /><ref name=":8" /> However, the computational complexity of these algorithms are dependent on the number of propositions (classes), and can lead a much higher computation time when compared to other machine learning approaches.

=== Training models ===
Typically, machine learning models require a high quantity of reliable data in order for the models to perform accurate predictions. When training a machine learning model, machine learning engineers need to target and collect a large and representative [[Sample (statistics)|sample]] of data. Data from the training set can be as varied as a corpus of text, a collection of images, [[Engineering:Sensor|sensor]] data, and data collected from individual users of a service. [[Overfitting]] is something to watch out for when training a machine learning model. Trained models derived from biased or non-evaluated data can result in skewed or undesired predictions. Bias models may result in detrimental outcomes thereby furthering the negative impacts on society or objectives. [[Algorithmic bias]] is a potential result of data not being fully prepared for training. Machine learning ethics is becoming a field of study and notably be integrated within machine learning engineering teams.

==== Federated learning ====
{{Main|Federated learning}}
Federated learning is an adapted form of [[Distributed artificial intelligence|distributed artificial intelligence]] to training machine learning models that decentralizes the training process, allowing for users' privacy to be maintained by not needing to send their data to a centralized server. This also increases efficiency by decentralizing the training process to many devices. For example, [[Software:Gboard|Gboard]] uses federated machine learning to train search query prediction models on users' mobile phones without having to send individual searches back to [[Company:Google|Google]].<ref>{{Cite web|url=http://ai.googleblog.com/2017/04/federated-learning-collaborative.html|title=Federated Learning: Collaborative Machine Learning without Centralized Training Data|website=Google AI Blog|date=6 April 2017 |language=en|access-date=2019-06-08|archive-date=2019-06-07|archive-url=https://web.archive.org/web/20190607054623/https://ai.googleblog.com/2017/04/federated-learning-collaborative.html|url-status=live}}</ref>

== Applications ==
There are many applications for machine learning, including:
{{cols|colwidth=21em}}
* [[Earth:Precision agriculture|Agriculture]]
* [[Biology:Computational anatomy|Anatomy]]
* [[Social:Adaptive website|Adaptive website]]
* Affective computing
* [[Astronomy:Astroinformatics|Astronomy]]
* [[Automated decision-making]]
* [[Finance:Banking|Banking]]
* [[Philosophy:Behaviorism|Behaviorism]]
* [[Biology:Bioinformatics|Bioinformatics]]
* [[Brain–computer interface|Brain–machine interfaces]]
* [[Chemistry:Cheminformatics|Cheminformatics]]
* Citizen Science
* Climate Science
* [[Network simulation|Computer networks]]
* [[Computer vision]]
* Credit-card fraud detection
* [[Data quality]]
* DNA sequence classification
* [[Finance:Computational economics|Economics]]
* [[Finance:Financial market|Financial market]] analysis<ref>Machine learning is included in the CFA Curriculum (discussion is top-down); see: [https://www.cfainstitute.org/-/media/documents/study-session/2020-l2-ss3.ashx Kathleen DeRose and Christophe Le Lanno (2020). "Machine Learning"] {{Webarchive|url=https://web.archive.org/web/20200113085425/https://www.cfainstitute.org/-/media/documents/study-session/2020-l2-ss3.ashx |date=2020-01-13 }}.</ref>
* [[General game playing]]
* [[Software:Handwriting recognition|Handwriting recognition]]
* [[Medicine:Artificial intelligence in healthcare|Healthcare]]
* [[Information retrieval]]
* [[Finance:Insurance|Insurance]]
* Internet fraud detection
* [[Knowledge graph embedding]]
* [[Computational linguistics|Linguistics]]
* [[Machine learning control]]
* [[Machine perception]]
* [[Machine translation]]
* [[Finance:Marketing|Marketing]]
* Medical diagnosis
* [[Natural language processing]]
* [[Natural-language understanding|Natural language understanding]]
* [[Finance:Online advertising|Online advertising]]
* [[Mathematical optimization|Optimization]]
* [[Recommender system]]s
* [[Engineering:Robot locomotion|Robot locomotion]]
* Search engines
* [[Sentiment analysis]]
* Sequence mining
* [[Software engineering]]
* [[Speech recognition]]
* [[Engineering:Structural health monitoring|Structural health monitoring]]
* [[Syntactic pattern recognition]]
* [[Engineering:Telecommunication|Telecommunication]]
* [[Automated theorem proving|Theorem proving]]
* [[Time series|Time-series forecasting]]
* [[Tomographic reconstruction]]<ref>{{cite journal |last1= Ivanenko |first1= Mikhail |last2= Smolik |first2= Waldemar T. |last3= Wanta |first3= Damian |last4= Midura |first4= Mateusz |last5= Wróblewski |first5= Przemysław  |last6= Hou |first6= Xiaohan |last7= Yan |first7= Xiaoheng |date= 2023 |title= Image Reconstruction Using Supervised Learning in Wearable Electrical Impedance Tomography of the Thorax  |journal= Sensors |volume= 23|issue= 18|page= 7774|doi= 10.3390/s23187774|pmid= 37765831 |pmc= 10538128 |bibcode= 2023Senso..23.7774I |doi-access= free}}</ref>
* [[User behavior analytics]]
{{colend}}

In 2006, the media-services provider [[Company:Netflix|Netflix]] held the first "Netflix Prize" competition to find a program to better predict user preferences and improve the accuracy of its existing Cinematch movie recommendation algorithm by at least 10%. A joint team made up of researchers from AT&T Labs-Research in collaboration with the teams Big Chaos and Pragmatic Theory built an ensemble model to win the Grand Prize in 2009 for $1 million.<ref>[https://web.archive.org/web/20151110062742/http://www2.research.att.com/~volinsky/netflix/ "BelKor Home Page"] research.att.com</ref> Shortly after the prize was awarded, Netflix realized that viewers' ratings were not the best indicators of their viewing patterns ("everything is a recommendation") and they changed their recommendation engine accordingly.<ref>{{cite web|url=http://techblog.netflix.com/2012/04/netflix-recommendations-beyond-5-stars.html|title=The Netflix Tech Blog: Netflix Recommendations: Beyond the 5 stars (Part 1)|access-date=8 August 2015|date=2012-04-06|archive-url=https://web.archive.org/web/20160531002916/http://techblog.netflix.com/2012/04/netflix-recommendations-beyond-5-stars.html|archive-date=31 May 2016}}</ref> In 2010 The Wall Street Journal wrote about the firm Rebellion Research and their use of machine learning to predict the financial crisis.<ref>{{cite web|url=https://www.wsj.com/articles/SB10001424052748703834604575365310813948080|title=Letting the Machines Decide|author=Scott Patterson|date=13 July 2010|publisher={{wipe|The Wall Street Journal}}|access-date=24 June 2018|archive-date=24 June 2018|archive-url=https://web.archive.org/web/20180624151019/https://www.wsj.com/articles/SB10001424052748703834604575365310813948080|url-status=live}}</ref> In 2012, co-founder of [[Company:Sun Microsystems|Sun Microsystems]], Vinod Khosla, predicted that 80% of medical doctors jobs would be lost in the next two decades to automated machine learning medical diagnostic software.<ref>{{cite web|url=https://techcrunch.com/2012/01/10/doctors-or-algorithms/|author=Vinod Khosla|publisher=Tech Crunch|title=Do We Need Doctors or Algorithms?|date=January 10, 2012|access-date=October 20, 2016|archive-date=June 18, 2018|archive-url=https://web.archive.org/web/20180618175811/https://techcrunch.com/2012/01/10/doctors-or-algorithms/|url-status=live}}</ref> In 2014, it was reported that a machine learning algorithm had been applied in the field of art history to study fine art paintings and that it may have revealed previously unrecognized influences among artists.<ref>[https://medium.com/the-physics-arxiv-blog/when-a-machine-learning-algorithm-studied-fine-art-paintings-it-saw-things-art-historians-had-never-b8e4e7bf7d3e When A Machine Learning Algorithm Studied Fine Art Paintings, It Saw Things Art Historians Had Never Noticed] {{Webarchive|url=https://web.archive.org/web/20160604072143/https://medium.com/the-physics-arxiv-blog/when-a-machine-learning-algorithm-studied-fine-art-paintings-it-saw-things-art-historians-had-never-b8e4e7bf7d3e |date=2016-06-04 }}, ''The Physics at [[ArXiv]] blog''</ref> In 2019 [[Company:Springer Nature|Springer Nature]] published the first research book created using machine learning.<ref>{{Cite web|url=https://www.theverge.com/2019/4/10/18304558/ai-writing-academic-research-book-springer-nature-artificial-intelligence|title=The first AI-generated textbook shows what robot writers are actually good at|last=Vincent|first=James|date=2019-04-10|website=The Verge|access-date=2019-05-05|archive-date=2019-05-05|archive-url=https://web.archive.org/web/20190505200409/https://www.theverge.com/2019/4/10/18304558/ai-writing-academic-research-book-springer-nature-artificial-intelligence|url-status=live}}</ref> In 2020, machine learning technology was used to help make diagnoses and aid researchers in developing a cure for COVID-19.<ref>{{Cite journal|title=Artificial Intelligence (AI) applications for COVID-19 pandemic|date=July 1, 2020|journal=Diabetes & Metabolic Syndrome: Clinical Research & Reviews|volume=14|issue=4|pages=337–339|doi=10.1016/j.dsx.2020.04.012|doi-access=free|last1=Vaishya|first1=Raju|last2=Javaid|first2=Mohd|last3=Khan|first3=Ibrahim Haleem|last4=Haleem|first4=Abid|pmid=32305024|pmc=7195043}}</ref> Machine learning was recently applied to predict the pro-environmental behavior of travelers.<ref>{{Cite journal|title=Application of machine learning to predict visitors' green behavior in marine protected areas: evidence from Cyprus|first1=Hamed|last1=Rezapouraghdam|first2=Arash|last2=Akhshik|first3=Haywantee|last3=Ramkissoon|date=March 10, 2021|journal=Journal of Sustainable Tourism|volume=31 |issue=11 |pages=2479–2505|doi=10.1080/09669582.2021.1887878|doi-access=free|hdl=10037/24073|hdl-access=free}}</ref> Recently, machine learning technology was also applied to optimize smartphone's performance and thermal behavior based on the user's interaction with the phone.<ref>{{Cite book|last1=Dey|first1=Somdip|last2=Singh|first2=Amit Kumar|last3=Wang|first3=Xiaohang|last4=McDonald-Maier|first4=Klaus|title=2020 Design, Automation & Test in Europe Conference & Exhibition (DATE) |chapter=User Interaction Aware Reinforcement Learning for Power and Thermal Efficiency of CPU-GPU Mobile MPSoCs |date=2020-06-15|chapter-url=https://ieeexplore.ieee.org/document/9116294|pages=1728–1733|doi=10.23919/DATE48585.2020.9116294|isbn=978-3-9819263-4-7|s2cid=219858480|url=http://repository.essex.ac.uk/27546/1/User%20Interaction%20Aware%20Reinforcement%20Learning.pdf |access-date=2022-01-20|archive-date=2021-12-13|archive-url=https://web.archive.org/web/20211213192526/https://ieeexplore.ieee.org/document/9116294/|url-status=live}}</ref><ref>{{Cite news|last=Quested|first=Tony|title=Smartphones get smarter with Essex innovation|work=Business Weekly|url=https://www.businessweekly.co.uk/news/academia-research/smartphones-get-smarter-essex-innovation|access-date=2021-06-17|archive-date=2021-06-24|archive-url=https://web.archive.org/web/20210624200126/https://www.businessweekly.co.uk/news/academia-research/smartphones-get-smarter-essex-innovation|url-status=live}}</ref><ref>{{Cite news|last=Williams|first=Rhiannon|date=2020-07-21|title=Future smartphones 'will prolong their own battery life by monitoring owners' behaviour'|url=https://inews.co.uk/news/technology/future-smartphones-prolong-battery-life-monitoring-behaviour-558689|access-date=2021-06-17|newspaper=i|language=en|archive-date=2021-06-24|archive-url=https://web.archive.org/web/20210624201153/https://inews.co.uk/news/technology/future-smartphones-prolong-battery-life-monitoring-behaviour-558689|url-status=live}}</ref> When applied correctly, machine learning algorithms (MLAs) can utilize a wide range of company characteristics to predict stock returns without [[Overfitting|overfitting]]. By employing effective feature engineering and combining forecasts, MLAs can generate results that far surpass those obtained from basic linear techniques like [[Ordinary least squares|OLS]].<ref>{{Cite journal |last1=Rasekhschaffe |first1=Keywan Christian |last2=Jones |first2=Robert C. |date=2019-07-01 |title=Machine Learning for Stock Selection |url=https://www.tandfonline.com/doi/full/10.1080/0015198X.2019.1596678 |journal=Financial Analysts Journal |language=en |volume=75 |issue=3 |pages=70–88 |doi=10.1080/0015198X.2019.1596678 |s2cid=108312507 |issn=0015-198X}}</ref>

== Limitations ==
Although machine learning has been transformative in some fields, machine-learning programs often fail to deliver expected results.<ref>{{Cite news|url=https://www.bloomberg.com/news/articles/2016-11-10/why-machine-learning-models-often-fail-to-learn-quicktake-q-a|title=Why Machine Learning Models Often Fail to Learn: QuickTake Q&A|date=2016-11-10|work=Bloomberg.com|access-date=2017-04-10|archive-url=https://web.archive.org/web/20170320225010/https://www.bloomberg.com/news/articles/2016-11-10/why-machine-learning-models-often-fail-to-learn-quicktake-q-a|archive-date=2017-03-20}}</ref><ref>{{Cite news|url=https://hbr.org/2017/04/the-first-wave-of-corporate-ai-is-doomed-to-fail|title=The First Wave of Corporate AI Is Doomed to Fail|date=2017-04-18|work=Harvard Business Review|access-date=2018-08-20|archive-date=2018-08-21|archive-url=https://web.archive.org/web/20180821032004/https://hbr.org/2017/04/the-first-wave-of-corporate-ai-is-doomed-to-fail|url-status=live}}</ref><ref>{{Cite news|url=https://venturebeat.com/2016/09/17/why-the-a-i-euphoria-is-doomed-to-fail/|title=Why the A.I. euphoria is doomed to fail|date=2016-09-18|work=VentureBeat|access-date=2018-08-20|language=en-US|archive-date=2018-08-19|archive-url=https://web.archive.org/web/20180819124138/https://venturebeat.com/2016/09/17/why-the-a-i-euphoria-is-doomed-to-fail/|url-status=live}}</ref> Reasons for this are numerous: lack of (suitable) data, lack of access to the data, data bias, privacy problems, badly chosen tasks and algorithms, wrong tools and people, lack of resources, and evaluation problems.<ref>{{Cite web|url=https://www.kdnuggets.com/2018/07/why-machine-learning-project-fail.html|title=9 Reasons why your machine learning project will fail|website=www.kdnuggets.com|language=en-US|access-date=2018-08-20|archive-date=2018-08-21|archive-url=https://web.archive.org/web/20180821031802/https://www.kdnuggets.com/2018/07/why-machine-learning-project-fail.html|url-status=live}}</ref>

The "[[Black box|black box theory]]" poses another yet significant challenge. Black box refers to a situation where the algorithm or the process of producing an output is entirely opaque, meaning that even the coders of the algorithm cannot audit the pattern that the machine extracted out of the data.<ref name=":12">{{Cite report |url=https://www.jstor.org/stable/resrep37375.8 |title=Transparency and Intelligibility |last1=Babuta |first1=Alexander |last2=Oswald |first2=Marion |date=2018 |publisher=Royal United Services Institute (RUSI) |pages=17–22 |last3=Rinik |first3=Christine}}</ref> The House of Lords Select Committee, which claimed that such an “intelligence system” that could have a “substantial impact on an individual’s life” would not be considered acceptable unless it provided “a full and satisfactory explanation for the decisions” it makes.<ref name=":12" />

In 2018, a self-driving car from [[Company:Uber|Uber]] failed to detect a pedestrian, who was killed after a collision.<ref>{{Cite news|url=https://www.economist.com/the-economist-explains/2018/05/29/why-ubers-self-driving-car-killed-a-pedestrian|title=Why Uber's self-driving car killed a pedestrian|newspaper=The Economist|access-date=2018-08-20|language=en|archive-date=2018-08-21|archive-url=https://web.archive.org/web/20180821031818/https://www.economist.com/the-economist-explains/2018/05/29/why-ubers-self-driving-car-killed-a-pedestrian|url-status=live}}</ref> Attempts to use machine learning in healthcare with the [[Engineering:Watson (computer)|IBM Watson]] system failed to deliver even after years of time and billions of dollars invested.<ref>{{Cite news|url=https://www.statnews.com/2018/07/25/ibm-watson-recommended-unsafe-incorrect-treatments/|title=IBM's Watson recommended 'unsafe and incorrect' cancer treatments – STAT|date=2018-07-25|work=STAT|access-date=2018-08-21|language=en-US|archive-date=2018-08-21|archive-url=https://web.archive.org/web/20180821062616/https://www.statnews.com/2018/07/25/ibm-watson-recommended-unsafe-incorrect-treatments/|url-status=live}}</ref><ref>{{Cite news|url=https://www.wsj.com/articles/ibm-bet-billions-that-watson-could-improve-cancer-treatment-it-hasnt-worked-1533961147|title=IBM Has a Watson Dilemma|last1=Hernandez|first1=Daniela|date=2018-08-11|work={{wipe|The Wall Street Journal}}|access-date=2018-08-21|last2=Greenwald|first2=Ted|language=en-US|issn=0099-9660|archive-date=2018-08-21|archive-url=https://web.archive.org/web/20180821031906/https://www.wsj.com/articles/ibm-bet-billions-that-watson-could-improve-cancer-treatment-it-hasnt-worked-1533961147|url-status=live}}</ref> Microsoft's chatbot has been reported to produce hostile and offensive response against its users.<ref>{{Cite web |last=Allyn |first=Bobby |date=Feb 27, 2023 |title=How Microsoft's experiment in artificial intelligence tech backfired |url=https://www.npr.org/2023/02/27/1159630243/how-microsofts-experiment-in-artificial-intelligence-tech-backfired |access-date=Dec 8, 2023 |website=National Public Radio}}</ref>

Machine learning has been used as a strategy to update the evidence related to a systematic review and increased reviewer burden related to the growth of biomedical literature. While it has improved with training sets, it has not yet developed sufficiently to reduce the workload burden without limiting the necessary sensitivity for the findings research themselves.<ref>{{Cite journal|last1=Reddy|first1=Shivani M.|last2=Patel|first2=Sheila|last3=Weyrich|first3=Meghan|last4=Fenton|first4=Joshua|last5=Viswanathan|first5=Meera|date=2020|title=Comparison of a traditional systematic review approach with review-of-reviews and semi-automation as strategies to update the evidence|url= |journal=Systematic Reviews|language=en|volume=9|issue=1|pages=243|doi=10.1186/s13643-020-01450-2|issn=2046-4053|pmc=7574591|pmid=33076975 |doi-access=free }}</ref>

=== Bias ===

Language models learned from data have been shown to contain human-like biases.<ref>{{Cite journal |last1=Caliskan |first1=Aylin |last2=Bryson |first2=Joanna J. |last3=Narayanan |first3=Arvind |date=2017-04-14 |title=Semantics derived automatically from language corpora contain human-like biases |journal=Science |language=en |volume=356 |issue=6334 |pages=183–186 |arxiv=1608.07187 |bibcode=2017Sci...356..183C |doi=10.1126/science.aal4230 |issn=0036-8075 |pmid=28408601 |s2cid=23163324}}</ref><ref>{{Citation |last1=Wang |first1=Xinan |title=An algorithm for L1 nearest neighbor search via monotonic embedding |date=2016 |url=http://papers.nips.cc/paper/6227-an-algorithm-for-l1-nearest-neighbor-search-via-monotonic-embedding.pdf |work=Advances in Neural Information Processing Systems 29 |pages=983–991 |editor-last=Lee |editor-first=D. D. |access-date=2018-08-20 |archive-url=https://web.archive.org/web/20170407051313/http://papers.nips.cc/paper/6227-an-algorithm-for-l1-nearest-neighbor-search-via-monotonic-embedding.pdf |url-status=live |publisher=Curran Associates, Inc. |archive-date=2017-04-07 |last2=Dasgupta |first2=Sanjoy |editor2-last=Sugiyama |editor2-first=M. |editor3-last=Luxburg |editor3-first=U. V. |editor4-last=Guyon |editor4-first=I.}}</ref> In an experiment carried out by ProPublica, an investigative journalism organization, a machine learning algorithm’s insight towards the recidivism rates among prisoners falsely flagged “black defendants high risk twice as often as white defendants.”<ref name=":22">{{Cite journal |last1=Silva |first1=Selena |last2=Kenney |first2=Martin |date=2018 |title=Algorithms, Platforms, and Ethnic Bias: An Integrative Essay |url=https://brie.berkeley.edu/sites/default/files/brie_wp_2018-3.pdf |journal=Phylon |volume=55 |issue=1 & 2 |pages=9–37 |jstor=26545017 |issn=0031-8906 |url-status=live |archive-url=https://web.archive.org/web/20240127200319/https://brie.berkeley.edu/sites/default/files/brie_wp_2018-3.pdf |archive-date= Jan 27, 2024 }}</ref> In 2015, Google photos would often tag black people as gorillas,<ref name=":22" /> and in 2018 this still was not well resolved, but Google reportedly was still using the workaround to remove all gorillas from the training data, and thus was not able to recognize real gorillas at all.<ref>{{Cite news |title=Google 'fixed' its racist algorithm by removing gorillas from its image-labeling tech |work=The Verge |url=https://www.theverge.com/2018/1/12/16882408/google-racist-gorillas-photo-recognition-algorithm-ai |date=Jan 12, 2018 |first1=James |last1=Vincent |url-status=live |access-date=2018-08-20 |archive-url=https://web.archive.org/web/20180821031830/https://www.theverge.com/2018/1/12/16882408/google-racist-gorillas-photo-recognition-algorithm-ai |archive-date=2018-08-21}}</ref> Similar issues with recognizing non-white people have been found in many other systems.<ref>{{Cite news |last1=Crawford |first1=Kate |date=25 June 2016 |title=Opinion {{!}} Artificial Intelligence's White Guy Problem |language=en |work={{wipe|New York Times}} |url=https://www.nytimes.com/2016/06/26/opinion/sunday/artificial-intelligences-white-guy-problem.html |url-access=subscription |url-status=live |access-date=2018-08-20 |archive-url=https://web.archive.org/web/20210114220619/https://www.nytimes.com/2016/06/26/opinion/sunday/artificial-intelligences-white-guy-problem.html |archive-date=2021-01-14}}</ref> In 2016, Microsoft tested a [[Chatbot|chatbot]] that learned from Twitter, and it quickly picked up racist and sexist language.<ref>{{Cite news |last=Metz |first=Rachel |title=Why Microsoft Accidentally Unleashed a Neo-Nazi Sexbot |date=March 24, 2016 |language=en |work=MIT Technology Review |url=https://www.technologyreview.com/s/601111/why-microsoft-accidentally-unleashed-a-neo-nazi-sexbot/ |url-access=limited |url-status=live |access-date=2018-08-20 |archive-url=https://web.archive.org/web/20181109023754/https://www.technologyreview.com/s/601111/why-microsoft-accidentally-unleashed-a-neo-nazi-sexbot/ |archive-date=2018-11-09}}</ref>

Because of such challenges, the effective use of machine learning may take longer to be adopted in other domains.<ref>{{Cite news |last=Simonite |first=Tom |title=Microsoft: AI Isn’t Yet Adaptable Enough to Help Businesses |date=March 30, 2017 |language=en |work=MIT Technology Review |url=https://www.technologyreview.com/s/603944/microsoft-ai-isnt-yet-adaptable-enough-to-help-businesses/ |url-status=live |access-date=2018-08-20 |archive-url=https://web.archive.org/web/20181109022820/https://www.technologyreview.com/s/603944/microsoft-ai-isnt-yet-adaptable-enough-to-help-businesses/ |archive-date=2018-11-09}}</ref> Concern for [[Fairness (machine learning)|fairness]] in machine learning, that is, reducing bias in machine learning and propelling its use for human good is increasingly expressed by artificial intelligence scientists, including [[Biography:Fei-Fei Li|Fei-Fei Li]], who reminds engineers that "There's nothing artificial about AI...It's inspired by people, it's created by people, and—most importantly—it impacts people. It is a powerful tool we are only just beginning to understand, and that is a profound responsibility."<ref>{{Cite news |last=Hempel |first=Jessi |date=2018-11-13 |title=Fei-Fei Li's Quest to Make Machines Better for Humanity |magazine=Wired |url=https://www.wired.com/story/fei-fei-li-artificial-intelligence-humanity/ |url-status=live |access-date=2019-02-17 |archive-url=https://web.archive.org/web/20201214095220/https://www.wired.com/story/fei-fei-li-artificial-intelligence-humanity/ |archive-date=2020-12-14 |issn=1059-1028}}</ref>

=== Explainability ===
{{Main|Explainable artificial intelligence}}

Explainable AI (XAI), or Interpretable AI, or Explainable Machine Learning (XML), is artificial intelligence (AI) in which humans can understand the decisions or predictions made by the AI.<ref>{{cite journal |last1=Rudin |first1=Cynthia |title=Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead |journal=Nature Machine Intelligence |date=2019 |volume=1 |issue=5 |pages=206–215 |doi=10.1038/s42256-019-0048-x |pmid=35603010 |pmc=9122117 }}</ref> It contrasts with the "black box" concept in machine learning where even its designers cannot explain why an AI arrived at a specific decision.<ref>{{cite journal |last1=Hu |first1=Tongxi |last2=Zhang |first2=Xuesong |last3=Bohrer |first3=Gil |last4=Liu |first4=Yanlan |last5=Zhou |first5=Yuyu |last6=Martin |first6=Jay |last7=LI |first7=Yang |last8=Zhao |first8=Kaiguang |title=Crop yield prediction via explainable AI and interpretable machine learning: Dangers of black box models for evaluating climate change impacts on crop yield|journal=Agricultural and Forest Meteorology |date=2023 |volume=336 |page=109458 |doi=10.1016/j.agrformet.2023.109458 |s2cid=258552400 |url=https://www.sciencedirect.com/science/article/pii/S0168192323001508}}</ref> By refining the mental models of users of AI-powered systems and dismantling their misconceptions, XAI promises to help users perform more effectively. XAI may be an implementation of the social right to explanation.

=== Overfitting ===
{{Main|Overfitting}}

[[File: Overfitted Data.png|thumb|The blue line could be an example of overfitting a linear function due to random noise.]]
Settling on a bad, overly complex theory gerrymandered to fit all the past training data is known as overfitting. Many systems attempt to reduce overfitting by rewarding a theory in accordance with how well it fits the data but penalizing the theory in accordance with how complex the theory is.{{sfn|Domingos|2015|loc=Chapter 6, Chapter 7}}

=== Other limitations and vulnerabilities ===
<!-- WHAT IS THE TECHNICAL TERM THAT DESCRIBES THIS LIMITATION? --> 
Learners can also disappoint by "learning the wrong lesson". A toy example is that an image classifier trained only on pictures of brown horses and black cats might conclude that all brown patches are likely to be horses.{{sfn|Domingos|2015|p=286}} A real-world example is that, unlike humans, current image classifiers often do not primarily make judgments from the spatial relationship between components of the picture, and they learn relationships between pixels that humans are oblivious to, but that still correlate with images of certain types of real objects. Modifying these patterns on a legitimate image can result in "adversarial" images that the system misclassifies.<ref>{{cite news|title=Single pixel change fools AI programs|url=https://www.bbc.com/news/technology-41845878|access-date=12 March 2018|work=BBC News|date=3 November 2017|archive-date=22 March 2018|archive-url=https://web.archive.org/web/20180322011306/http://www.bbc.com/news/technology-41845878|url-status=live}}</ref><ref>{{cite news|title=AI Has a Hallucination Problem That's Proving Tough to Fix|url=https://www.wired.com/story/ai-has-a-hallucination-problem-thats-proving-tough-to-fix/|access-date=12 March 2018|magazine=WIRED|date=2018|archive-date=12 March 2018|archive-url=https://web.archive.org/web/20180312024533/https://www.wired.com/story/ai-has-a-hallucination-problem-thats-proving-tough-to-fix/|url-status=live}}</ref>

<!-- WHAT IS THE TECHNICAL TERM THAT DESCRIBES THIS LIMITATION?  --> 
Adversarial vulnerabilities can also result in nonlinear systems, or from non-pattern perturbations. For some systems, it is possible to change the output by only changing a single adversarially chosen pixel.<ref name=TD_1>{{cite arXiv | title=Towards deep learning models resistant to adversarial attacks| author1=Madry, A.| author2=Makelov, A.| author3=Schmidt, L.| author4=Tsipras, D.| author5=Vladu, A. | date=4 September 2019| class=stat.ML| eprint=1706.06083}}</ref> Machine learning models are often vulnerable to manipulation and/or evasion via [[Adversarial machine learning|adversarial machine learning]].<ref>{{cite web |title=Adversarial Machine Learning – CLTC UC Berkeley Center for Long-Term Cybersecurity |url=https://cltc.berkeley.edu/aml/ |website=CLTC |access-date=2022-05-25 |archive-date=2022-05-17 |archive-url=https://web.archive.org/web/20220517045352/https://cltc.berkeley.edu/aml/ |url-status=live }}</ref>

Researchers have demonstrated how [[Backdoor (computing)|backdoors]] can be placed undetectably into classifying (e.g., for categories "spam" and well-visible "not spam" of posts) machine learning models which are often developed and/or trained by third parties. Parties can change the classification of any input, including in cases for which a type of [[Algorithmic transparency|data/software transparency]] is provided, possibly including [[White-box testing|white-box access]].<ref>{{cite news |title=Machine-learning models vulnerable to undetectable backdoors |url=https://www.theregister.com/2022/04/21/machine_learning_models_backdoors/ |access-date=13 May 2022 |work=The Register |language=en |archive-date=13 May 2022 |archive-url=https://web.archive.org/web/20220513171215/https://www.theregister.com/2022/04/21/machine_learning_models_backdoors/ |url-status=live }}</ref><ref>{{cite news |title=Undetectable Backdoors Plantable In Any Machine-Learning Algorithm |url=https://spectrum.ieee.org/machine-learningbackdoor |access-date=13 May 2022 |work=IEEE Spectrum |date=10 May 2022 |language=en |archive-date=11 May 2022 |archive-url=https://web.archive.org/web/20220511152052/https://spectrum.ieee.org/machine-learningbackdoor |url-status=live }}</ref><ref>{{Cite arXiv|last1=Goldwasser |first1=Shafi |last2=Kim |first2=Michael P. |last3=Vaikuntanathan |first3=Vinod |last4=Zamir |first4=Or |title=Planting Undetectable Backdoors in Machine Learning Models |date=14 April 2022|class=cs.LG |eprint=2204.06974 }}</ref>

== Model assessments ==
Classification of machine learning models can be validated by accuracy estimation techniques like the holdout method, which splits the data in a training and test set (conventionally 2/3 training set and 1/3 test set designation) and evaluates the performance of the training model on the test set. In comparison, the K-fold-[[Cross-validation (statistics)|cross-validation]] method randomly partitions the data into K subsets and then K experiments are performed each respectively considering 1 subset for evaluation and the remaining K-1 subsets for training the model. In addition to the holdout and cross-validation methods, [[Bootstrapping (statistics)|bootstrap]], which samples n instances with replacement from the dataset, can be used to assess model accuracy.<ref>{{cite journal|last1=Kohavi|first1=Ron|title=A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection|journal=International Joint Conference on Artificial Intelligence|date=1995|url=https://ai.stanford.edu/~ronnyk/accEst.pdf|access-date=2023-03-26|archive-date=2018-07-12|archive-url=https://web.archive.org/web/20180712102706/http://web.cs.iastate.edu/~jtian/cs573/Papers/Kohavi-IJCAI-95.pdf|url-status=live}}</ref>

In addition to overall accuracy, investigators frequently report [[Sensitivity and specificity|sensitivity and specificity]] meaning True Positive Rate (TPR) and True Negative Rate (TNR) respectively. Similarly, investigators sometimes report the [[False positive rate|false positive rate]] (FPR) as well as the false negative rate (FNR). However, these rates are ratios that fail to reveal their numerators and denominators. The [[Total operating characteristic|total operating characteristic]] (TOC) is an effective method to express a model's diagnostic ability. TOC shows the numerators and denominators of the previously mentioned rates, thus TOC provides more information than the commonly used [[Receiver operating characteristic|receiver operating characteristic]] (ROC) and ROC's associated area under the curve (AUC).<ref>{{cite journal|last1=Pontius|first1=Robert Gilmore|last2=Si|first2=Kangping|title=The total operating characteristic to measure diagnostic ability for multiple thresholds| journal=International Journal of Geographical Information Science|volume=28|issue=3|year=2014|pages=570–583|doi=10.1080/13658816.2013.862623|bibcode=2014IJGIS..28..570P |s2cid=29204880}}</ref>

== Ethics ==
Machine learning poses a host of [[Machine ethics|ethical questions]]. Systems that are trained on datasets collected with biases may exhibit these biases upon use ([[Algorithmic bias|algorithmic bias]]), thus digitizing cultural prejudices.<ref>{{Cite web|url=http://www.nickbostrom.com/ethics/artificial-intelligence.pdf|title=The Ethics of Artificial Intelligence|last=Bostrom|first=Nick|date=2011|access-date=11 April 2016|archive-url=https://web.archive.org/web/20160304015020/http://www.nickbostrom.com/ethics/artificial-intelligence.pdf|archive-date=4 March 2016}}</ref> For example, in 1988, the UK's Commission for Racial Equality found that St. George's Medical School had been using a computer program trained from data of previous admissions staff and this program had denied nearly 60 candidates who were found to be either women or had non-European sounding names.<ref name=":15"/> Using job hiring data from a firm with racist hiring policies may lead to a machine learning system duplicating the bias by scoring job applicants by similarity to previous successful applicants.<ref name="Edionwe Outline">{{cite web|last1=Edionwe|first1=Tolulope|title=The fight against racist algorithms|url=https://theoutline.com/post/1571/the-fight-against-racist-algorithms|website=The Outline|access-date=17 November 2017|archive-date=17 November 2017|archive-url=https://web.archive.org/web/20171117174504/https://theoutline.com/post/1571/the-fight-against-racist-algorithms|url-status=live}}</ref><ref name="Jeffries Outline">{{cite web|last1=Jeffries|first1=Adrianne|title=Machine learning is racist because the internet is racist|url=https://theoutline.com/post/1439/machine-learning-is-racist-because-the-internet-is-racist|website=The Outline|access-date=17 November 2017|archive-date=17 November 2017|archive-url=https://web.archive.org/web/20171117174503/https://theoutline.com/post/1439/machine-learning-is-racist-because-the-internet-is-racist|url-status=live}}</ref> Another example includes predictive policing company [[Company:Geolitica|Geolitica]]'s predictive algorithm that resulted in “disproportionately high levels of over-policing in low-income and minority communities” after being trained with historical crime data.<ref name=":22" />

While responsible [[Data collection|collection of data]] and documentation of algorithmic rules used by a system is considered a critical part of machine learning, some researchers blame lack of participation and representation of minority population in the field of AI for machine learning's vulnerability to biases.<ref>{{Cite journal |last=Wong |first=Carissa |date=2023-03-30 |title=AI 'fairness' research held back by lack of diversity |url=https://www.nature.com/articles/d41586-023-00935-z |journal=Nature |language=en |doi=10.1038/d41586-023-00935-z|pmid=36997714 |s2cid=257857012 }}</ref> In fact, according to research carried out by the Computing Research Association (CRA) in 2021, “female faculty merely make up 16.1%” of all faculty members who focus on AI among several universities around the world.<ref name=":32">{{Cite journal |last=Zhang |first=Jack Clark |title=Artificial Intelligence Index Report 2021 |url=https://aiindex.stanford.edu/wp-content/uploads/2021/11/2021-AI-Index-Report_Master.pdf |journal=Stanford Institute for Human-Centered Artificial Intelligence}}</ref> Furthermore, among the group of “new U.S. resident AI PhD graduates,” 45% identified as white, 22.4% as Asian, 3.2% as Hispanic, and 2.4% as African American, which further demonstrates a lack of diversity in the field of AI.<ref name=":32" />

AI can be well-equipped to make decisions in technical fields, which rely heavily on data and historical information. These decisions rely on objectivity and logical reasoning.<ref>{{cite web |url=https://www.nickbostrom.com/ethics/artificial-intelligence.pdf |title=THE ETHICS OF ARTIFICIAL INTELLIGENCE |date=2011 |first1=Nick |last1=Bostrom |first2=Eliezer |last2=Yudkowsky |website=Nick Bostrom |access-date=2020-11-18 |archive-date=2015-12-20 |archive-url=https://web.archive.org/web/20151220175220/http://www.nickbostrom.com/ethics/artificial-intelligence.pdf |url-status=live }}</ref> Because human languages contain biases, machines trained on language ''[[Text corpus|corpora]]'' will necessarily also learn these biases.<ref>{{cite arXiv|eprint=1809.02208|class=cs.CY |author=M.O.R. Prates |author2=P.H.C. Avelar |author3=L.C. Lamb |title=Assessing Gender Bias in Machine Translation – A Case Study with Google Translate|date=11 Mar 2019}}</ref><ref>{{cite web |url=https://freedom-to-tinker.com/2016/08/24/language-necessarily-contains-human-biases-and-so-will-machines-trained-on-language-corpora/ |title=Language necessarily contains human biases, and so will machines trained on language corpora |date=August 24, 2016 |first=Arvind |last=Narayanan |website=Freedom to Tinker |access-date=November 19, 2016 |archive-date=June 25, 2018 |archive-url=https://web.archive.org/web/20180625021555/https://freedom-to-tinker.com/2016/08/24/language-necessarily-contains-human-biases-and-so-will-machines-trained-on-language-corpora/ |url-status=live }}</ref>

Other forms of ethical challenges, not related to personal biases, are seen in health care. There are concerns among health care professionals that these systems might not be designed in the public's interest but as income-generating machines.<ref>{{Cite journal|last1=Char|first1=Danton S.|last2=Shah|first2=Nigam H.|last3=Magnus|first3=David|date=2018-03-15|title=Implementing Machine Learning in Health Care — Addressing Ethical Challenges|url= |journal=New England Journal of Medicine|language=en|volume=378|issue=11|pages=981–983|doi=10.1056/NEJMp1714229|issn=0028-4793|pmc=5962261|pmid=29539284}}</ref> This is especially true in the United States where there is a long-standing ethical dilemma of improving health care, but also increasing profits. For example, the algorithms could be designed to provide patients with unnecessary tests or medication in which the algorithm's proprietary owners hold stakes. There is potential for machine learning in health care to provide professionals an additional tool to diagnose, medicate, and plan recovery paths for patients, but this requires these biases to be mitigated.<ref>{{cite journal |last1=Char |first1=D. S. |last2=Shah |first2=N. H. |last3=Magnus |first3=D. |year=2018 |title=Implementing Machine Learning in Health Care—Addressing Ethical Challenges |journal=New England Journal of Medicine |volume=378 |issue=11 |pages=981–983 |doi=10.1056/nejmp1714229 |pmid=29539284 |pmc=5962261 }}</ref>

== Hardware ==
Since the 2010s, advances in both machine learning algorithms and computer hardware have led to more efficient methods for training deep neural networks (a particular narrow subdomain of machine learning) that contain many layers of non-linear hidden units.<ref>{{cite web|last1=Research|first1=AI|title=Deep Neural Networks for Acoustic Modeling in Speech Recognition|url=http://airesearch.com/ai-research-papers/deep-neural-networks-for-acoustic-modeling-in-speech-recognition/|website=airesearch.com|access-date=23 October 2015|date=23 October 2015|archive-date=1 February 2016|archive-url=https://web.archive.org/web/20160201033801/http://airesearch.com/ai-research-papers/deep-neural-networks-for-acoustic-modeling-in-speech-recognition/|url-status=live}}</ref> By 2019, graphic processing units (GPUs), often with AI-specific enhancements, had displaced CPUs as the dominant method of training large-scale commercial cloud AI.<ref>{{cite news |title=GPUs Continue to Dominate the AI Accelerator Market for Now |url=https://www.informationweek.com/big-data/ai-machine-learning/gpus-continue-to-dominate-the-ai-accelerator-market-for-now/a/d-id/1336475 |access-date=11 June 2020 |work=InformationWeek |date=December 2019 |language=en |archive-date=10 June 2020 |archive-url=https://web.archive.org/web/20200610094310/https://www.informationweek.com/big-data/ai-machine-learning/gpus-continue-to-dominate-the-ai-accelerator-market-for-now/a/d-id/1336475 |url-status=live }}</ref> [[Company:OpenAI|OpenAI]] estimated the hardware computing used in the largest deep learning projects from AlexNet (2012) to AlphaZero (2017), and found a 300,000-fold increase in the amount of compute required, with a doubling-time trendline of 3.4 months.<ref>{{cite news |last1=Ray |first1=Tiernan |title=AI is changing the entire nature of compute |url=https://www.zdnet.com/article/ai-is-changing-the-entire-nature-of-compute/ |access-date=11 June 2020 |work=ZDNet |date=2019 |language=en |archive-date=25 May 2020 |archive-url=https://web.archive.org/web/20200525144635/https://www.zdnet.com/article/ai-is-changing-the-entire-nature-of-compute/ |url-status=live }}</ref><ref>{{cite web |title=AI and Compute |url=https://openai.com/blog/ai-and-compute/ |website=OpenAI |access-date=11 June 2020 |language=en |date=16 May 2018 |archive-date=17 June 2020 |archive-url=https://web.archive.org/web/20200617200602/https://openai.com/blog/ai-and-compute/ |url-status=live }}</ref>

===Neuromorphic/Physical Neural Networks===

A [[Physical neural network|physical neural network]] or [[Neuromorphic engineering|Neuromorphic computer]]  is a type of [[Artificial neural network|artificial neural network]] in which an electrically adjustable material is used to emulate the function of a [[Biology:Chemical synapse|neural synapse]]. "Physical" neural network is used to emphasize the reliance on physical hardware used to emulate neurons as opposed to software-based approaches. More generally the term is applicable to other artificial neural networks in which a [[Engineering:Memristor|memristor]] or other electrically adjustable resistance material is used to emulate a neural synapse.<ref>{{Cite web|url = https://syncedreview.com/2021/05/27/deepmind-podracer-tpu-based-rl-frameworks-deliver-exceptional-performance-at-low-cost-28/|title = Cornell & NTT's Physical Neural Networks: A "Radical Alternative for Implementing Deep Neural Networks" That Enables Arbitrary Physical Systems Training &#124; Synced|date = 27 May 2021|access-date = 12 October 2021|archive-date = 27 October 2021|archive-url = https://web.archive.org/web/20211027183428/https://syncedreview.com/2021/05/27/deepmind-podracer-tpu-based-rl-frameworks-deliver-exceptional-performance-at-low-cost-28/|url-status = live}}</ref><ref>{{Cite web|url=https://www.theregister.com/2021/10/05/analogue_neural_network_research/|title=Nano-spaghetti to solve neural network power consumption|access-date=2021-10-12|archive-date=2021-10-06|archive-url=https://web.archive.org/web/20211006150057/https://www.theregister.com/2021/10/05/analogue_neural_network_research/|url-status=live}}</ref>

===Embedded Machine Learning===
'''Embedded Machine Learning''' is a sub-field of machine learning, where the machine learning model is run on embedded systems with limited computing resources such as [[Wearable computer|wearable computer]]s, [[Edge device|edge device]]s and microcontrollers.<ref>{{Cite book|last1=Fafoutis|first1=Xenofon|last2=Marchegiani|first2=Letizia|last3=Elsts|first3=Atis|last4=Pope|first4=James|last5=Piechocki|first5=Robert|last6=Craddock|first6=Ian|title=2018 IEEE 4th World Forum on Internet of Things (WF-IoT) |chapter=Extending the battery lifetime of wearable sensors with embedded machine learning |date=2018-05-07|chapter-url=https://ieeexplore.ieee.org/document/8355116|pages=269–274|doi=10.1109/WF-IoT.2018.8355116|hdl=1983/b8fdb58b-7114-45c6-82e4-4ab239c1327f|isbn=978-1-4673-9944-9|s2cid=19192912|url=https://research-information.bris.ac.uk/en/publications/b8fdb58b-7114-45c6-82e4-4ab239c1327f |access-date=2022-01-17|archive-date=2022-01-18|archive-url=https://web.archive.org/web/20220118182543/https://ieeexplore.ieee.org/abstract/document/8355116?casa_token=LCpUeGLS1e8AAAAA:2OjuJfNwZBnV2pgDxfnEAC-jbrETv_BpTcX35_aFqN6IULFxu1xbYbVSRpD-zMd4GCUMELyG|url-status=live}}</ref><ref>{{Cite web|date=2021-06-02|title=A Beginner's Guide To Machine learning For Embedded Systems|url=https://analyticsindiamag.com/a-beginners-guide-to-machine-learning-for-embedded-systems/|access-date=2022-01-17|website=Analytics India Magazine|language=en-US|archive-date=2022-01-18|archive-url=https://web.archive.org/web/20220118182754/https://analyticsindiamag.com/a-beginners-guide-to-machine-learning-for-embedded-systems/|url-status=live}}</ref><ref>{{Cite web|last=Synced|date=2022-01-12|title=Google, Purdue & Harvard U's Open-Source Framework for TinyML Achieves up to 75x Speedups on FPGAs {{!}} Synced|url=https://syncedreview.com/2022/01/12/deepmind-podracer-tpu-based-rl-frameworks-deliver-exceptional-performance-at-low-cost-183/|access-date=2022-01-17|website=syncedreview.com|language=en-US|archive-date=2022-01-18|archive-url=https://web.archive.org/web/20220118182404/https://syncedreview.com/2022/01/12/deepmind-podracer-tpu-based-rl-frameworks-deliver-exceptional-performance-at-low-cost-183/|url-status=live}}</ref> Running machine learning model in embedded devices removes the need for transferring and storing data on cloud servers for further processing, henceforth, reducing data breaches and privacy leaks happening because of transferring data, and also minimizes theft of intellectual properties, personal data and business secrets. Embedded Machine Learning could be applied through several techniques including [[Hardware acceleration|hardware acceleration]],<ref>{{Cite book|last1=Giri|first1=Davide|last2=Chiu|first2=Kuan-Lin|last3=Di Guglielmo|first3=Giuseppe|last4=Mantovani|first4=Paolo|last5=Carloni|first5=Luca P.|title=2020 Design, Automation & Test in Europe Conference & Exhibition (DATE) |chapter=ESP4ML: Platform-Based Design of Systems-on-Chip for Embedded Machine Learning |date=2020-06-15|chapter-url=https://ieeexplore.ieee.org/document/9116317|pages=1049–1054|doi=10.23919/DATE48585.2020.9116317|arxiv=2004.03640|isbn=978-3-9819263-4-7|s2cid=210928161|access-date=2022-01-17|archive-date=2022-01-18|archive-url=https://web.archive.org/web/20220118182342/https://ieeexplore.ieee.org/abstract/document/9116317?casa_token=5I_Tmgrrbu4AAAAA:v7pDHPEWlRuo2Vk3pU06194PO0-W21UOdyZqADrZxrRdPBZDMLwQrjJSAHUhHtzJmLu_VdgW|url-status=live}}</ref><ref>{{Cite web|last1=Louis|first1=Marcia Sahaya|last2=Azad|first2=Zahra|last3=Delshadtehrani|first3=Leila|last4=Gupta|first4=Suyog|last5=Warden|first5=Pete|last6=Reddi|first6=Vijay Janapa|last7=Joshi|first7=Ajay|date=2019|title=Towards Deep Learning using TensorFlow Lite on RISC-V|url=https://edge.seas.harvard.edu/publications/towards-deep-learning-using-tensorflow-lite-risc-v|access-date=2022-01-17|website=[[Organization:Harvard University|Harvard University]]|archive-date=2022-01-17|archive-url=https://web.archive.org/web/20220117031909/https://edge.seas.harvard.edu/publications/towards-deep-learning-using-tensorflow-lite-risc-v|url-status=live}}</ref> using [[Approximate computing|approximate computing]],<ref>{{Cite book|last1=Ibrahim|first1=Ali|last2=Osta|first2=Mario|last3=Alameh|first3=Mohamad|last4=Saleh|first4=Moustafa|last5=Chible|first5=Hussein|last6=Valle|first6=Maurizio|title=2018 25th IEEE International Conference on Electronics, Circuits and Systems (ICECS) |chapter=Approximate Computing Methods for Embedded Machine Learning |date=2019-01-21|chapter-url=https://ieeexplore.ieee.org/document/8617877|pages=845–848|doi=10.1109/ICECS.2018.8617877|isbn=978-1-5386-9562-3|s2cid=58670712|access-date=2022-01-17|archive-date=2022-01-17|archive-url=https://web.archive.org/web/20220117031855/https://ieeexplore.ieee.org/abstract/document/8617877?casa_token=arUW5Oy-tzwAAAAA:I9x6edlfskM6kGNFUN9zAFrjEBv_8kYTz7ERTxtXu9jAqdrYCcDbbwjBdgwXvb6QAH_-0VJJ|url-status=live}}</ref> optimization of machine learning models and many more.<ref>{{Cite web|title=dblp: TensorFlow Eager: A Multi-Stage, Python-Embedded DSL for Machine Learning.|url=https://dblp.org/rec/journals/corr/abs-1903-01855.html|access-date=2022-01-17|website=dblp.org|language=en|archive-date=2022-01-18|archive-url=https://web.archive.org/web/20220118182335/https://dblp.org/rec/journals/corr/abs-1903-01855.html|url-status=live}}</ref><ref>{{Cite journal|last1=Branco|first1=Sérgio|last2=Ferreira|first2=André G.|last3=Cabral|first3=Jorge|date=2019-11-05|title=Machine Learning in Resource-Scarce Embedded Systems, FPGAs, and End-Devices: A Survey|journal=Electronics|volume=8|issue=11|pages=1289|doi=10.3390/electronics8111289|issn=2079-9292|doi-access=free|hdl=1822/62521|hdl-access=free}}</ref>

== Software ==
Software suites containing a variety of machine learning algorithms include the following:

=== Free and open-source software{{anchor|Open-source_software}} ===
{{Div col|colwidth=18em}}
* [[Software:Caffe|Caffe]]
* [[Software:Deeplearning4j|Deeplearning4j]]
* [[Software:DeepSpeed|DeepSpeed]]
* [[Software:ELKI|ELKI]]
* [[Software:Google JAX|Google JAX]]
* [[Software:Infer.NET|Infer.NET]]
* [[Software:Keras|Keras]]
* [[Software:Kubeflow|Kubeflow]]
* [[Software:LightGBM|LightGBM]]
* [[Software:Apache Mahout|Mahout]]
* [[Software:Mallet (software project)|Mallet]] 
* [[Software:Microsoft Cognitive Toolkit|Microsoft Cognitive Toolkit]]
* [[Software:ML.NET|ML.NET]]
* [[Software:Mlpack|mlpack]]
* MXNet
* [[Software:OpenNN|OpenNN]]
* [[Software:Orange|Orange]]
* [[Software:Pandas|pandas (software)]]
* [[Software:ROOT|ROOT]] (TMVA with ROOT)
* [[Software:Scikit-learn|scikit-learn]]
* [[Software:Shogun (toolbox)|Shogun]]
* [[Software:Apache Spark#MLlib Machine Learning Library|Spark MLlib]]
* [[Software:Apache SystemML|SystemML]]
* [[Software:TensorFlow|TensorFlow]]
* [[Software:Torch (machine learning)|Torch]] / [[Software:PyTorch|PyTorch]]
* [[Software:Weka (machine learning)|Weka]] / MOA
* [[Software:XGBoost|XGBoost]]
* [[Software:Yooreeka|Yooreeka]]
{{Div col end}}

=== Proprietary software with free and open-source editions ===
* [[Software:KNIME|KNIME]]
* [[Software:RapidMiner|RapidMiner]]

=== Proprietary software ===
{{Div col|colwidth=18em}}
* Amazon Machine Learning
* [[Company:Angoss|Angoss]] KnowledgeSTUDIO
* Azure Machine Learning
* IBM Watson Studio
* [[Google Cloud Platform#Cloud AI|Google Cloud Vertex AI]]
* [[Google APIs|Google Prediction API]]
* [[Software:SPSS Modeler|IBM SPSS Modeler]]
* [[Software:KXEN Inc.|KXEN Modeler]]
* [[Software:LIONsolver|LIONsolver]]
* [[Software:Mathematica|Mathematica]]
* [[Software:MATLAB|MATLAB]]
* [[Software:Neural Designer|Neural Designer]]
* [[Software:NeuroSolutions|NeuroSolutions]]
* [[Software:Oracle Data Mining|Oracle Data Mining]]
* [[Software:Oracle Cloud#Platform as a Service (PaaS)|Oracle AI Platform Cloud Service]]
* [[Software:PolyAnalyst|PolyAnalyst]]
* [[RCASE]]
* [[Software:SAS#Components|SAS Enterprise Miner]]
* [[Software:SequenceL|SequenceL]]
* [[Company:Splunk|Splunk]]
* STATISTICA Data Miner
{{Div col end}}

== Journals ==
* [[Journal of Machine Learning Research]]
* Machine Learning
* [[Nature Machine Intelligence]]
* Neural Computation
* IEEE Transactions on Pattern Analysis and Machine Intelligence

== Conferences ==
* AAAI Conference on Artificial Intelligence
* [[Organization:Association for Computational Linguistics|Association for Computational Linguistics ('''ACL''')]]
* European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases ('''ECML PKDD''')
* International Conference on Computational Intelligence Methods for Bioinformatics and Biostatistics ('''CIBB''')
* International Conference on Machine Learning ('''ICML''')
* International Conference on Learning Representations ('''ICLR''')
* [[Engineering:International Conference on Intelligent Robots and Systems|International Conference on Intelligent Robots and Systems ('''IROS''')]]
* Conference on Knowledge Discovery and Data Mining ('''KDD''')
* [[Conference on Neural Information Processing Systems|Conference on Neural Information Processing Systems ('''NeurIPS''')]]

== See also ==
* {{annotated link|Automated machine learning}}
* {{annotated link|Big data}}
* {{annotated link|Differentiable programming}}
* [[Force control]]
* {{annotated link|List of datasets for machine-learning research}}

== References ==
{{Reflist|30em}}

== Sources ==
* {{cite book
| title =  The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World
| date = September 22, 2015
| publisher = Basic Books
| isbn = 978-0465065707
}}
* {{cite book|last=Nilsson|first=Nils|year=1998|title=Artificial Intelligence: A New Synthesis|url=https://archive.org/details/artificialintell0000nils|url-access=registration|publisher=Morgan Kaufmann|isbn=978-1-55860-467-4|access-date=18 November 2019|archive-date=26 July 2020|archive-url=https://web.archive.org/web/20200726131654/https://archive.org/details/artificialintell0000nils|url-status=live}}
* {{Russell Norvig 2003}}.
* {{cite book|first1=David|last1=Poole|first2=Alan|last2=Mackworth|first3=Randy|last3=Goebel|year=1998|title=Computational Intelligence: A Logical Approach|publisher=Oxford University Press|location=New York|isbn=978-0-19-510270-3|url=https://archive.org/details/computationalint00pool|access-date=22 August 2020|archive-date=26 July 2020|archive-url=https://web.archive.org/web/20200726131436/https://archive.org/details/computationalint00pool|url-status=live}}

== Further reading ==
{{refbegin|30em}}
*  Nils J. Nilsson, ''[https://ai.stanford.edu/people/nilsson/mlbook.html Introduction to Machine Learning] {{Webarchive|url=https://web.archive.org/web/20190816182600/http://ai.stanford.edu/people/nilsson/mlbook.html |date=2019-08-16 }}''.
* [[Biography:Trevor Hastie|Trevor Hastie]], [[Biography:Robert Tibshirani|Robert Tibshirani]] and [[Biography:Jerome H. Friedman|Jerome H. Friedman]] (2001). ''[https://web.stanford.edu/~hastie/ElemStatLearn/ The Elements of Statistical Learning] {{Webarchive|url=https://web.archive.org/web/20131027220938/http://www-stat.stanford.edu/%7Etibs/ElemStatLearn// |date=2013-10-27 }}'', Springer. {{ISBN|0-387-95284-5}}.
* [[Biography:Pedro Domingos|Pedro Domingos]] (September 2015), ''[[The Master Algorithm]]'', Basic Books, {{ISBN|978-0-465-06570-7}} 
* Ian H. Witten and Eibe Frank (2011). ''Data Mining: Practical machine learning tools and techniques'' Morgan Kaufmann, 664pp., {{ISBN|978-0-12-374856-0}}.
* Ethem Alpaydin (2004). ''Introduction to Machine Learning'', MIT Press, {{ISBN|978-0-262-01243-0}}.
* David J. C. MacKay. ''[http://www.inference.phy.cam.ac.uk/mackay/itila/book.html Information Theory, Inference, and Learning Algorithms] {{Webarchive|url=https://web.archive.org/web/20160217105359/http://www.inference.phy.cam.ac.uk/mackay/itila/book.html |date=2016-02-17 }}'' Cambridge: Cambridge University Press, 2003. {{ISBN|0-521-64298-1}}
* Richard O. Duda, Peter E. Hart, David G. Stork (2001) ''Pattern classification'' (2nd edition), Wiley, New York, {{ISBN|0-471-05669-3}}.
* [[Biography:Christopher Bishop|Christopher Bishop]] (1995). ''Neural Networks for Pattern Recognition'', Oxford University Press. {{ISBN|0-19-853864-2}}.
* Stuart Russell & Peter Norvig, (2009). ''[http://aima.cs.berkeley.edu/ Artificial Intelligence – A Modern Approach] {{Webarchive|url=https://web.archive.org/web/20110228023805/http://aima.cs.berkeley.edu/ |date=2011-02-28 }}''. Pearson, {{ISBN|9789332543515}}. 
* [[Biography:Ray Solomonoff|Ray Solomonoff]], ''An Inductive Inference Machine'', IRE Convention Record, Section on Information Theory, Part 2, pp., 56–62, 1957.
* [[Biography:Ray Solomonoff|Ray Solomonoff]], ''[http://world.std.com/~rjs/indinf56.pdf An Inductive Inference Machine] {{Webarchive|url=https://web.archive.org/web/20110426161749/http://world.std.com/~rjs/indinf56.pdf |date=2011-04-26 }}'' A privately circulated report from the 1956 [[Dartmouth workshop|Dartmouth Summer Research Conference on AI]].
* Kevin P. Murphy (2021). ''[https://probml.github.io/pml-book/book1.html Probabilistic Machine Learning: An Introduction] {{Webarchive|url=https://web.archive.org/web/20210411153246/https://probml.github.io/pml-book/book1.html |date=2021-04-11 }}'', MIT Press.
{{Refend}}

== External links ==
*[https://web.archive.org/web/20171230081341/http://machinelearning.org/ International Machine Learning Society]
*[https://mloss.org/ mloss] is an academic database of open-source machine learning software.

{{Differentiable computing}}
{{Computer science}}

[[Category:Machine learning| ]]
[[Category:Cybernetics]]
[[Category:Learning]]

{{Sourceattribution|Machine learning}}