  Single-channel deep speech enhancement approaches often estimate a single
multiplicative mask to extract clean speech without a measure of its accuracy.
Instead, in this work, we propose to quantify the uncertainty associated with
clean speech estimates in neural network-based speech enhancement. Predictive
uncertainty is typically categorized into aleatoric uncertainty and epistemic
uncertainty. The former accounts for the inherent uncertainty in data and the
latter corresponds to the model uncertainty. Aiming for robust clean speech
estimation and efficient predictive uncertainty quantification, we propose to
integrate statistical complex Gaussian mixture models (CGMMs) into a deep
speech enhancement framework. More specifically, we model the dependency
between input and output stochastically by means of a conditional probability
density and train a neural network to map the noisy input to the full posterior
distribution of clean speech, modeled as a mixture of multiple complex Gaussian
components. Experimental results on different datasets show that the proposed
algorithm effectively captures predictive uncertainty and that combining
powerful statistical models and deep learning also delivers a superior speech
enhancement performance.
