# variational mixture of Gaussians

(2.7 hours to learn)

## Summary

Variational Bayes EM can be applied to fitting a mixture of Gaussians model. Unlike standard mixture of Gaussians fit with EM, the variational algorithm automatically controls the model complexity and yields a lower bound on the marginal likelihood.

## Context

This concept has the prerequisites:

- variational Bayes
- mixture of Gaussians models
- Bayesian parameter estimation: multivariate Gaussians (The posterior over parameters for a multivariate Gaussian is part of the update rule for this model.)
- Bayesian parameter estimation: multinomial distribution (The posterior over the mixture probabilities is part of the update rule for this model.)

## Core resources (read/watch one of the following)

## -Paid-

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 10.2, pages 474-486

## Supplemental resources (the following are optional, but you may find them useful)

## -Paid-

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Section 21.6, pages 749-756

## See also

-No Additional Notes-