This note describes generalized expectation (GE) criteria, a framework for incorporating preferences about model expectations into parameter estimation objective functions. We discuss relations to other methods, various learning paradigms it supports, and applications that can leverage its flexibility.

Last week, we saw how we could represent clustering with a probabilistic model. In this model, called a Gaussian mixture model, we model each datapoint x i as originating from some cluster, with a corresponding cluster label y i distributed according to p(y), and the corresponding distribution for that cluster given by a multivariate Gaussian: p(x|y = k) =