Variational bounds via reversing EM

Thomas P. Minka
Talk given at JPRC 8/26/99

Variational bounds have proven to be a simple and efficient way to approximate integrals in statistical models. The EM algorithm can be viewed as a variational bounding method, but for maximization instead of integration. I extend this equivalence by showing that any EM algorithm for maximization can be "reversed" to yield a variational method for integration. Virtually all existing variational learning and ensemble learning algorithms can be interpreted in this way. Furthermore, the quality of the integrator is directly related to the convergence rate of the EM algorithm it came from. This perspective allows us to leverage recent advances in "fast EM" to get better integration algorithms.

For example, Pilla & Lindsay have recently proposed a fast EM algorithm for fitting mixture weights. I demonstrate how this algorithm can be reversed to marginalize out the weights in a mixture, which is useful for promoting simpler mixtures. I compare reverse EM to various incarnations of Laplace's method on this problem.

Postscript slides (85K)

Also see the paper "Variational Bayes for mixture models: Reversing EM".

Last modified: Fri Dec 10 14:24:36 GMT 2004