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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:

${\displaystyle P(x|h)={\begin{cases}{\frac {1}{|h|}}&{\text{, if }}x\in h\\0&{\text{, otherwise}}\end{cases}}}$

In weak sampling, we assume observations randomly sampled and then classified:

${\displaystyle P(x|h)={\begin{cases}1&{\text{, if }}x\in h\\0&{\text{, otherwise}}\end{cases}}}$

Consequence: Posterior computation under Weak Sampling

${\displaystyle P(h|x)={\frac {P(x|h)P(h)}{\sum \limits _{h'}P(x|h')P(h')}}={\begin{cases}{\frac {P(h)}{\sum \limits _{h':x\in h'}P(h')}}&{\text{, if }}x\in h\\0&{\text{, otherwise}}\end{cases}}}$

Therefore the likelihood ${\displaystyle P(x|h')}$ for all hypotheses ${\displaystyle h'}$ will be "ignored".

References

External links

• Lecture 20: Strong vs weak sampling

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