A Majorization-Minimization Algorithm for Estimating the Regularized Wavelet-based Density-Difference

摘要

In this paper, we propose a novel method for estimating the density-difference (DD) between two distributions represented in a wavelet basis expansion. This new Regularized Wavelet-based Density-Difference (RWDD) method directly estimates the DD using the l_2 distance between two distributions (expanded in a wavelet basis) without an explicit need to reconstruct the individual probabilities. We develop a regularized objective function that is balanced using both l_2 and l_1 norm penalties. Experimental evaluations on simulated noisy datasets, from complex multimodal to skewed distributions, clearly showed the superior performance of the proposed RWDD in comparison to other competing techniques.