Monte Carlo estimation
(1.1 hours to learn)
One way to answer queries about a probability distribution is to simulate from the distribution, a procedure known as Monte Carlo estimation. In particular, we estimate the expected value of some function f with respect to a distribution p by generating samples from p and averaging the values of f over those samples.
This concept has the prerequisites:
- expectation and variance (Monte Carlo methods are a way of estimating expectations.)
Core resources (read/watch one of the following)
→ Machine learning summer school: Markov chain Monte Carlo (2009)
A video tutorial on MCMC methods.
Location: up to 10:20
→ Information Theory, Inference, and Learning Algorithms
A graudate-level textbook on machine learning and information theory.
→ Machine Learning: a Probabilistic Perspective
A very comprehensive graudate-level machine learning textbook.
Location: Section 2.7, pages 52-56
Supplemental resources (the following are optional, but you may find them useful)
→ Coursera: Probabilistic Graphical Models (2013)
An online course on probabilistic graphical models.
Location: Lecture "Simple sampling"
- Click on "Preview" to see the videos.
→ Pattern Recognition and Machine Learning
A textbook for a graduate machine learning course, with a focus on Bayesian methods.
Location: Chapter 11 intro, pages 523-526
- The law of large numbers justifies the use of Monte Carlo estimation.
- Some commonly used sampling algorithms include:
- Gibbs sampling , a generic and widely applicable sampling algorithm
- particle filters , which are useful for time series modeling
- Metropolis-Hastings algorithm , which is very general
- variational inference , which tries to approximate an intractable posterior distribution with a tractable one
- loopy belief propagation , a strategy which is particular to graphical models
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