Simulated Annealing for Fitting Linear Combinations of Gaussians to Data

Abstract

 It is difficult to find a good fit of a combination of Gaussians to arbitrary empirical data. The surface defined by the objective function contains many local minima, which trap gradient descent algorithms and cause stochastic methods to tarry unreasonably in the vicinity. A number of techniques for accelerating convergence when using simulated annealing are presented. These are tested on a sample of known Gaussian combinations and are compared for accuracy and resource consumption. A single `best' set of techniques is found which gives good results on the test samples and on empirical data.