Learning mixture models via component-wise parameter smoothing

The task of obtaining an optimal set of parameters to fit a mixture model has many applications in science and engineering domains and is a computationally challenging problem. A novel algorithm using a convolution based smoothing approach to construct a hierarchy (or family) of smoothed log-likelihood surfaces is proposed. This approach smooths the likelihood function and applies the EM algorithm to obtain a promising solution on the smoothed surface. Using the most promising solutions as initial guesses, the EM algorithm is applied again on the original likelihood. Though the results are demonstrated using only two levels, the method can potentially be applied to any number of levels in the hierarchy. A theoretical insight demonstrates that the smoothing approach indeed reduces the overall gradient of a modified version of the likelihood surface. This optimization procedure effectively eliminates extensive searching in non-promising regions of the parameter space. Results on some benchmark datasets demonstrate significant improvements of the proposed algorithm compared to other approaches. Empirical results on the reduction in the number of local maxima and improvements in the initialization procedures are provided.