Created: July 05, 2022
Modified: July 05, 2022

importance sampling

This page is from my personal notes, and has not been specifically reviewed for public consumption. It might be incomplete, wrong, outdated, or stupid. Caveat lector.

Importance sampling allows us to compute expectations under a distribution $p$ using samples from a different distribution $q$ , by weighting the samples by the ratio of their probabilities:

\tilde{F}(x) = \frac{1}{N}\sum_{i=1}^N \frac{p(x_i)}{q(x_i)} f(x_i); \qquad x_i\sim q

so that $\tilde{F}$ is an unbiased estimate of $f(x)$ ,

\mathbb{E}_{x\sim q}[\tilde{F}(x)] = \mathbb{E}_{x\sim p}[f(x)].

The ratios $w_i = \frac{p(x_i)}{q(x_i)}$ are sometimes called the importance weights.

importance sampling

Links to this note

priors are conceptual attention

trust region policy optimization

weighted importance sampling

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