Sequential Monte Carlo samplers for marginal likelihood computation in multiplicative exponential noise models

Model scoring in latent factor models is essential for a broad spectrum of applications such as clustering, change point detection or model order estimation. In a Bayesian setting, model selection is achieved via computation of the marginal likelihood. However, this is a typically challenging task as it involves calculation of a multidimensional integral over all the latent variables. In this paper, we consider approximate computation of the conditional marginal likelihood in a multiplicative exponential noise model, which is the generative model for latent factor models with the Itakura-Saito divergence such as the Nonnegative Matrix Factorization (NMF). We show that standard approaches are not accurate and propose two new methods in the sequential Monte Carlo (SMC) samplers framework. We explore the performances of these estimators on two problems.