Sampling Methods for Unsupervised Learning

We present an algorithm to overcome the local maxima problem in es- timating the parameters of mixture models. It combines existing ap- proaches from both EM and a robust tting algorithm, RANSAC, to give a data-driven stochastic learning scheme. Minimal subsets of data points, sufcient to constrain the parameters of the model, are drawn from pro- posal densities to discover new regions of high likelihood. The proposal densities are learnt using EM and bias the sampling toward promising solutions. The algorithm is computationally efcient, as well as effective at escaping from local maxima. We compare it with alternative methods, including EM and RANSAC, on both challenging synthetic data and the computer vision problem of alpha-matting.