Infinite Factorial Unbounded-State Hidden Markov Model

THERE are several real-world problems in which an observed temporal sequence can be explained by several unobservable independent causes, and we are interested in describing the latent model that leads to these observations. Two examples are trading in financial markets and energy disaggregation. An observer or participant in financial markets only sees the quotes1 of the orders placed by other participants. Orders are anonymous, so it is not generally possible to know who is on the other side of a transaction and how many other offers have been placed by the same trader. However, it is desirable to know the structure of the market from a trading and financial stability point of view. In the energy disaggregation problem, we observe the whole-home power signal, and we want to separate it into the power signals of the individual devices, because several studies have shown that providing consumers with detailed power use information at the device level can significantly improve energy efficiency [1], [2]. Hidden Markov models (HMMs) characterize time varying sequences with a simple yet powerful latent variable model [3]. HMMs have been a major success story in many fields involving complex sequential data, including speech and handwriting recognition (see, e.g., [4], [5]), computational molecular biology [6] and natural language processing (see, e.g., [7]). In most of these applications, the model topology is determined in advance and the model parameters are estimated by an expectation maximization (EM) procedure [8], which its particularization is also known as the Baum-Welch (or forward-backward) algorithm [9]. However, both the standard estimation procedure and the model definition for HMMs suffer from important limitations as not considering the complexity of the model (making it hard to avoid over or underfitting) and needing to pre-specify the model structure. In [10] the authors proposed an inference algorithm for HMMs based on reversible jump Markov chain Monte Carlo (RJMCMC) techniques [11] to address the model selection problem, which can be used to estimate both the parameters and the number of hidden states of an HMM in a Bayesian framework.