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Calculating expectations is frequent task in Machine Learning. Monte Carlo methods are some of our most effective approaches to this problem, but they can suffer from high variance estimates. Importance Sampling is a clever technique to obtain lower variance estimates.

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SOURCES

[1] was my primary source. Chapter 17 of [2] and chapter 23 of [3] provided a useful discussion more directed at the use cases of Machine Learning.

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[1] E. Anderson, "Monte Carlo Methods and Importance Sampling", [ Ссылка ]

[2] I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning, MIT Press, 2016

[3] K. P. Murphy. Machine Learning: A Probabilistic Perspective, MIT Press, 2012

TIMESTAMP
0:00 Intro
0:16 Monte Carlo Methods
2:29 Monte Carlo Example
3:57 Distribution of Monte Carlo Estimate
6:06 Importance Sampling
9:00 Importance Sampling Example
11:40 When to use Importance Sampling

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