Francisco Jesús Rodríguez Ruíz, a PhD student in the Signal Processing Group of the University Carlos III de Madrid has defended his doctoral thesis titled “Bayesian nonparametrics for time series modeling” on June, 30th
- Title: “Bayesian nonparametrics for time series modeling“
- Advisor: Fernando Pérez Cruz.
- Event Date: Tuesday, June 30, 2015, 11:30 am.
- Location: Sala de Vídeo, Biblioteca 3.1.S08 Leganés Campus; Universidad Carlos III de Madrid.
In many real-world signal processing problems, an observed temporal sequence can be explained by several unobservable independent causes, and we are interested in recovering the canonical signals that lead to these observations. For example, we may want to separate the overlapping voices on a single recording, distinguish the individual players on a financial market, or recover the underlying brain signals from electroencephalography data. This problem, known as source separation, is in general highly underdetermined or ill-posed. Methods for source separation generally seek to narrow the set of possible solutions in a way that is unlikely to exclude the desired solution.
However, most classical approaches for source separation assume a fixed and known number of latent sources. This may represent a limitation in contexts in which the number of independent causes is unknown and is not limited to a small range. In this Thesis, we address the signal separation problem from a probabilistic modeling perspective. We encode our independence assumptions in a probabilistic model and develop inference algorithms to unveil the underlying sequences that explain the observed signal. We adopt a Bayesian nonparametric (BNP) approach in order to let the inference procedure estimate the number of independent sequences that best explain the data.
BNP models place a prior distribution over an infinite-dimensional parameter space, which makes them particularly useful in probabilistic models in which the number of hidden parameters is unknown a priori. Under this prior distribution, the posterior distribution of the hidden parameters given the data assigns higher probability mass to those configurations that best explain the observations. Hence, inference over the hidden variables is performed using standard Bayesian inference techniques, which avoids expensive model selection steps.
We develop two novel BNP models for source separation in time series. First, we propose a non-binary infinite factorial hidden Markov model (IFHMM), in which the number of parallel chains of a factorial hidden Markov model (FHMM) is treated in a nonparametric fashion. This model constitutes an extension of the binary IFHMM, but the hidden states are not restricted to take binary values.
Moreover, by placing a Poisson prior distribution over the cardinality of the hidden states, we develop the infinite factorial unbounded-state hidden Markov model (IFUHMM), and an inference algorithm that can infer both the number of chains and the number of states in the factorial model. Second, we introduce the infinite factorial finite state machine (IFFSM) model, in which the number of independent Markov chains is also potentially infinite, but each of them evolves according to a stochastic finite-memory finite state machine model. For the IFFSM, we apply an efficient inference algorithm, based on particle Markov chain Monte Carlo (MCMC) methods, that avoids the exponential runtime complexity of more standard MCMC algorithms such as forward-filtering backward-sampling.
Although our models are applicable in a broad range of fields, we focus on two specific problems: power disaggregation and multiuser channel estimation and symbol detection. The power disaggregation problem consists in estimating the power draw of individual devices, given the aggregate whole-home power consumption signal. Blind multiuser channel estimation and symbol detection involves inferring the channel coefficients and the transmitted symbol in a multiuser digital communication system, such as a wireless communication network, with no need of training data. We assume that the number of electrical devices or the number of transmitters is not known in advance. Our experimental results show that the proposed methodology can provide accurate results, outperforming state-of-the-art approaches.