A dynamic latent variable model for source separation

We propose a novel latent variable model for learning latent bases for time-varying non-negative data. Our model uses a mixture multinomial as the likelihood function and proposes a Dirichlet distribution with dynamic parameters as a prior, which we call the dynamic Dirichlet prior. An expectation maximization (EM) algorithm is developed for estimating the parameters of the proposed model. Furthermore, we connect our proposed dynamic Dirichlet latent variable model (dynamic DLVM) to the two popular latent basis learning methods - probabilistic latent component analysis (PLCA) and non-negative matrix factorization (NMF). We show that (i) PLCA is a special case of the dynamic DLVM, and (ii) dynamic DLVM can be interpreted as a dynamic version of NMF. The effectiveness of the proposed model is demonstrated through extensive experiments on speaker source separation, and speech-noise separation. In both cases, our method performs better than relevant and competitive baselines. For speaker separation, dynamic DLVM shows 1.38 dB improvement in terms of source to interference ratio, and 1 dB improvement in source to artifact ratio

Dirichlet latent variable model : a dynamic model based on Dirichlet prior for audio processing

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 (i) PLCA is a special case of our DLVM, and (ii) 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 out performs several relevant existing methods in all three applications

Probabilistic sequential matrix factorization

We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space models where sequential approximate inference results in the factorization of a data matrix into a dictionary and time-varying coefficients with potentially nonlinear Markovian dependencies. The assumed Markovian structure on the coefficients enables us to encode temporal dependencies into a low-dimensional feature space. The proposed inference method is solely based on an approximate extended Kalman filtering scheme, which makes the resulting method particularly efficient. PSMF can account for temporal nonlinearities and, more importantly, can be used to calibrate and estimate generic differentiable nonlinear subspace models. We also introduce a robust version of PSMF, called rPSMF, which uses Student-t filters to handle model misspecification. We show that PSMF can be used in multiple contexts: modeling time series with a periodic subspace, robustifying changepoint detection methods, and imputing missing data in several high-dimensional time-series, such as measurements of pollutants across London.Comment: Accepted for publication at AISTATS 202

A state-space approach to dynamic nonnegative matrix factorization

Nonnegative matrix factorization (NMF) has been actively investigated and used in a wide range of problems in the past decade. A significant amount of attention has been given to develop NMF algorithms that are suitable to model time series with strong temporal dependencies. In this paper, we propose a novel state-space approach to perform dynamic NMF (D-NMF). In the proposed probabilistic framework, the NMF coefficients act as the state variables and their dynamics are modeled using a multi-lag nonnegative vector autoregressive (N-VAR) model within the process equation. We use expectation maximization and propose a maximum-likelihood estimation framework to estimate the basis matrix and the N-VAR model parameters. Interestingly, the N-VAR model parameters are obtained by simply applying NMF. Moreover, we derive a maximum a posteriori estimate of the state variables (i.e., the NMF coefficients) that is based on a prediction step and an update step, similarly to the Kalman filter. We illustrate the benefits of the proposed approach using different numerical simulations where D-NMF significantly outperforms its static counterpart. Experimental results for three different applications show that the proposed approach outperforms two state-of-the-art NMF approaches that exploit temporal dependencies, namely a nonnegative hidden Markov model and a frame stacking approach, while it requires less memory and computational power.QC 20141219</p