Inference in Hidden Markov Models with Explicit State Duration Distributions

In this letter we borrow from the inference techniques developed for unbounded state-cardinality (nonparametric) variants of the HMM and use them to develop a tuning-parameter free, black-box inference procedure for Explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have latent states consisting of both discrete state-indicator and discrete state-duration random variables. In contrast to the implicit geometric state duration distribution possessed by the standard HMM, EDHMMs allow the direct parameterisation and estimation of per-state duration distributions. As most duration distributions are defined over the positive integers, truncation or other approximations are usually required to perform EDHMM inference

Stochastic Collapsed Variational Inference for Sequential Data

Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm in the sequential data setting. Our algorithm is applicable to both finite hidden Markov models and hierarchical Dirichlet process hidden Markov models, and to any datasets generated by emission distributions in the exponential family. Our experiment results on two discrete datasets show that our inference is both more efficient and more accurate than its uncollapsed version, stochastic variational inference.Comment: NIPS Workshop on Advances in Approximate Bayesian Inference, 201

Learning Tree Distributions by Hidden Markov Models

Hidden tree Markov models allow learning distributions for tree structured data while being interpretable as nondeterministic automata. We provide a concise summary of the main approaches in literature, focusing in particular on the causality assumptions introduced by the choice of a specific tree visit direction. We will then sketch a novel non-parametric generalization of the bottom-up hidden tree Markov model with its interpretation as a nondeterministic tree automaton with infinite states.Comment: Accepted in LearnAut2018 worksho

Reinforcement Learning of Speech Recognition System Based on Policy Gradient and Hypothesis Selection

Speech recognition systems have achieved high recognition performance for several tasks. However, the performance of such systems is dependent on the tremendously costly development work of preparing vast amounts of task-matched transcribed speech data for supervised training. The key problem here is the cost of transcribing speech data. The cost is repeatedly required to support new languages and new tasks. Assuming broad network services for transcribing speech data for many users, a system would become more self-sufficient and more useful if it possessed the ability to learn from very light feedback from the users without annoying them. In this paper, we propose a general reinforcement learning framework for speech recognition systems based on the policy gradient method. As a particular instance of the framework, we also propose a hypothesis selection-based reinforcement learning method. The proposed framework provides a new view for several existing training and adaptation methods. The experimental results show that the proposed method improves the recognition performance compared to unsupervised adaptation.Comment: 5 pages, 6 figure

A reversible infinite HMM using normalised random measures

We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected we define a prior over random walks on graphs that results in a reversible Markov chain. The resulting prior over infinite transition matrices is closely related to the hierarchical Dirichlet process but enforces reversibility. A reinforcement scheme has recently been proposed with similar properties, but the de Finetti measure is not well characterised. We take the alternative approach of explicitly constructing the mixing measure, which allows more straightforward and efficient inference at the cost of no longer having a closed form predictive distribution. We use our process to construct a reversible infinite HMM which we apply to two real datasets, one from epigenomics and one ion channel recording.Comment: 9 pages, 6 figure

A Nonparametric Bayesian Approach to Uncovering Rat Hippocampal Population Codes During Spatial Navigation

Rodent hippocampal population codes represent important spatial information about the environment during navigation. Several computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. Here we extend our previous work and propose a nonparametric Bayesian approach to infer rat hippocampal population codes during spatial navigation. To tackle the model selection problem, we leverage a nonparametric Bayesian model. Specifically, to analyze rat hippocampal ensemble spiking activity, we apply a hierarchical Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference methods, one based on Markov chain Monte Carlo (MCMC) and the other based on variational Bayes (VB). We demonstrate the effectiveness of our Bayesian approaches on recordings from a freely-behaving rat navigating in an open field environment. We find that MCMC-based inference with Hamiltonian Monte Carlo (HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and MCMC approaches with hyperparameters set by empirical Bayes