Beta Process Sparse Nonnegative Matrix Factorization for Music

Nonnegative matrix factorization (NMF) has been widely used for discovering physically meaningful latent components in audio signals to facilitate source separation. Most of the existing NMF algorithms require that the number of latent components is provided a priori, which is not always possible. In this paper, we leverage developments from the Bayesian nonparametrics and compressive sensing literature to propose a probabilistic Beta Process Sparse NMF (BP-NMF) model, which can automatically infer the proper number of latent components based on the data. Unlike previous models, BP-NMF explicitly assumes that these latent components are often completely silent. We derive a novel mean-field variational inference algorithm for this nonconjugate model and evaluate it on both synthetic data and real recordings on various tasks.