Dirichlet Latent Variable Model: A Dynamic Model Based on Dirichlet Prior for Audio Processing

Abstract

We propose a dynamic latent variable model for learning latent bases from time varying, non-negative data. We take a probabilistic approach to modeling the temporal dependence in data by introducing a dynamic Dirichlet prior—a Dirichlet distribution with dynamic parameters. This new distribution allows us to assure non-negativity and avoid intractability when sequential updates are performed otherwise encountered in using Dirichlet prior. We refer to the proposed model as the Dirichlet latent variable model DLVM. We develop an expectation maximization algorithm for the proposed model, and also derive a maximum a posteriori estimate of the parameters. Furthermore, we connect the proposed DLVM to two popular latent basis learning methods—probabilistic latent component analysis PLCA and non-negative matrix factorization NMF. We show that 1 PLCA is a special case of our DLVM, and 2 DLVM can be interpreted as a dynamic version of NMF. The usefulness of DLVM is demonstrated for three audio processing applications—speaker source separation, denoising, and bandwidth expansion. To this end, a new algorithm for source separation is also proposed. Through extensive experiments on benchmark databases, we show that the proposed model outperforms several relevant existing methods in all three applications.