A Maximum Likelihood Approach to Deep Neural Network Based Nonlinear Spectral Mapping for Single-Channel Speech Separation

In contrast to the conventional minimum mean squared error (MMSE) training criterion for nonlinear spectral mapping based on deep neural networks (DNNs), we propose a probabilistic learning framework to estimate the DNN parameters for singlechannel speech separation. A statistical analysis of the prediction error vector at the DNN output reveals that it follows a unimodal density for each log power spectral component. By characterizing the prediction error vector as a multivariate Gaussian density with zero mean vector and an unknown covariance matrix, we present a maximum likelihood (ML) approach to DNN parameter learning. Our experiments on the Speech Separation Challenge (SSC) corpus show that the proposed learning approach can achieve a better generalization capability and a faster convergence than MMSE-based DNN learning. Furthermore, we demonstrate that the ML-trained DNN consistently outperforms MMSE-trained DNN in all the objective measures of speech quality and intelligibility in single-channel speech separation.