  Speech enhancement in the time-frequency domain is often performed by
estimating a multiplicative mask to extract clean speech. However, most neural
network-based methods perform point estimation, i.e., their output consists of
a single mask. In this paper, we study the benefits of modeling uncertainty in
neural network-based speech enhancement. For this, our neural network is
trained to map a noisy spectrogram to the Wiener filter and its associated
variance, which quantifies uncertainty, based on the maximum a posteriori (MAP)
inference of spectral coefficients. By estimating the distribution instead of
the point estimate, one can model the uncertainty associated with each
estimate. We further propose to use the estimated Wiener filter and its
uncertainty to build an approximate MAP (A-MAP) estimator of spectral
magnitudes, which in turn is combined with the MAP inference of spectral
coefficients to form a hybrid loss function to jointly reinforce the
estimation. Experimental results on different datasets show that the proposed
method can not only capture the uncertainty associated with the estimated
filters, but also yield a higher enhancement performance over comparable models
that do not take uncertainty into account.
