We propose the infinite factorial dynamic model (iFDM), a general Bayesian nonparametric model for source separation. Our model builds on the Markov Indian buffet process to consider a potentially unbounded number of hidden Markov chains (sources) that evolve independently according to some dynamics, in which the state space can be either discrete or continuous. For posterior inference, we develop an algorithm based on particle Gibbs with ancestor sampling that can be efficiently applied to a wide range of source separation problems. We evaluate the performance of our iFDM on four well-known applications: multitarget tracking, cocktail party, power disaggregation, and multiuser detection. Our experimental results show that our approach for source separation does not only outperform previous approaches, but it can also handle problems that were computationally intractable for existing approaches.

We propose the infinite factorial dynamic model (iFDM), a general Bayesian nonparametric model for source separation. Our model builds on the Markov Indian buffet process to consider a potentially unbounded number of hidden Markov chains (sources) that evolve independently according to some dynamics, in which the state space can be either discrete or continuous. For posterior inference, we develop an algorithm based on particle Gibbs with ancestor sampling that can be efficiently applied to a wide range of source separation problems. We evaluate the performance of our iFDM on four well-known applications: multitarget tracking, cocktail party, power disaggregation, and multiuser detection. Our experimental results show that our approach for source separation does not only outperform previous approaches, but it can also handle problems that were computationally intractable for existing approaches.

We propose the infinite factorial dynamic model (iFDM), a general Bayesian nonparametric model for source separation. Our model builds on the Markov Indian buffet process to consider a potentially unbounded number of hidden Markov chains (sources) that evolve independently according to some dynamics, in which the state space can be either discrete or continuous. For posterior inference, we develop an algorithm based on particle Gibbs with ancestor sampling that can be efficiently applied to a wide range of source separation problems. We evaluate the performance of our iFDM on four well-known applications: multitarget tracking, cocktail party, power disaggregation, and multiuser detection. Our experimental results show that our approach for source separation does not only outperform previous approaches, but it can also handle problems that were computationally intractable for existing approaches.

Factorial hidden Markov models (FHMMs) are powerful tools of modeling sequential data. Learning FHMMs yields a challenging simultaneous model selection issue, i.e., selecting the number of multiple Markov chains and the dimensionality of each chain. Our main contribution is to address this model selection issue by extending Factorized Asymptotic Bayesian (FAB) inference to FHMMs. First, we offer a better approximation of marginal log-likelihood than the previous FAB inference. Our key idea is to integrate out transition probabilities, yet still apply the Laplace approximation to emission probabilities. Second, we prove that if there are two very similar hidden states in an FHMM, i.e. one is redundant, then FAB will almost surely shrink and eliminate one of them, making the model parsimonious. Experimental results show that FAB for FHMMs significantly outperforms state-of-the-art nonparametric Bayesian iFHMM and Variational FHMM in model selection accuracy, with competitive held-out perplexity.

We introduces a new probability distribution over a potentially infinite number of binary Markov chains which we call the Markov Indian buffet process. This process extends the IBP to allow temporal dependencies in the hidden variables. We use this stochastic process to build a nonparametric extension of the factorial hidden Markov model. After working out an inference scheme which combines slice sampling and dynamic programming we demonstrate how the infinite factorial hidden Markov model can be used for blind source separation.