Poisson-uniform nonnegative matrix factorization

Probabilistic models of audio spectrograms used in audio source separation often rely on Poisson or multinomial noise models corresponding to the generalized Kullback-Leibler (GKL) divergence popular in methods using Nonnegative Matrix Factorization (NMF). This noise model works well in practice, but it is difficult to justify since these distribu-tions are technically only applicable to discrete counts data. This issue is particularly problematic in hierarchical and non-parametric Bayesian models where estimates of uncertainty depend strongly on the likelihood model. In this paper, we present a hierarchical Bayesian model that retains the flavor of the Poisson likelihood model but yields a coherent gener-ative process for continuous spectrogram data. This model allows for more principled, accurate, and effective Bayesian inference in probabilistic NMF models based on GKL. Index Terms — NMF, audio, Bayesian models, varia-tional inference, blind source separation