Strong and weak sampling
Strong and weak sampling are two sampling approach[1] in Statistics, and are popular in computational cognitive science and language learning.[2] In strong sampling, it is assumed that the data are intentionally generated as positive examples of a concept,[3] while in weak sampling, it is assumed that the data are generated without any restrictions.[4]
Formal Definition
In strong sampling, we assume observation is randomly sampled from the true hypothesis:
[math]\displaystyle{ P(x|h) = \begin{cases} \frac{1}{|h|} & \text{, if } x \in h \\ 0 & \text{, otherwise} \end{cases} }[/math]
In weak sampling, we assume observations randomly sampled and then classified:
[math]\displaystyle{ P(x|h) = \begin{cases} 1 & \text{, if } x \in h \\ 0 & \text{, otherwise} \end{cases} }[/math]
Consequence: Posterior computation under Weak Sampling
[math]\displaystyle{ P(h|x) = \frac{P(x|h) P(h)}{\sum\limits_{h'} P(x|h') P(h')} = \begin{cases} \frac{P(h)}{\sum\limits_{h': x \in h'} P(h')} & \text{, if } x \in h \\ 0 & \text{, otherwise} \end{cases} }[/math]
Therefore the likelihood [math]\displaystyle{ P(x|h') }[/math] for all hypotheses [math]\displaystyle{ h' }[/math] will be "ignored".
References
- ↑ Xu, Fei. "Bayesian word learning Sensitivity to sampling in Bayesian word learning". Developmental Science. https://web.mit.edu/cocosci/Papers/devsci07_xu_tenenbaum.pdf.
- ↑ Hsu, Anne. "Sampling assumptions in language learning 1 Running head: SAMPLING ASSUMPTIONS IN LANGUAGE LEARNING Sampling assumptions affect use of indirect negative evidence in language learning". https://www.researchgate.net/figure/Two-different-sampling-assumptions-for-language-learning-a-Under-the-weak-sampling_fig11_267829053.
- ↑ Navarro, Danielle. "Lecture 20: Strong vs weak sampling". https://compcogsci-3016.djnavarro.net/lecture20.pdf.
- ↑ Navarro, Daniel (2012). "Sampling assumptions in inductive generalization". Cognitive Science 36 (2): 187–223. doi:10.1111/j.1551-6709.2011.01212.x. PMID 22141440. https://pubmed.ncbi.nlm.nih.gov/22141440/.
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