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

Bayesian Nonparametric Hidden Semi-Markov Models

There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM's strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can extend the HDP-HMM to capture such structure by drawing upon explicit-duration semi-Markovianity, which has been developed mainly in the parametric frequentist setting, to allow construction of highly interpretable models that admit natural prior information on state durations. In this paper we introduce the explicit-duration Hierarchical Dirichlet Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for efficient posterior inference. The methods we introduce also provide new methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs sampling methods can be embedded in samplers for larger hierarchical Bayesian models, adding semi-Markov chain modeling as another tool in the Bayesian inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference methods on both synthetic and real experiments

Modeling Individual Cyclic Variation in Human Behavior

Cycles are fundamental to human health and behavior. However, modeling cycles in time series data is challenging because in most cases the cycles are not labeled or directly observed and need to be inferred from multidimensional measurements taken over time. Here, we present CyHMMs, a cyclic hidden Markov model method for detecting and modeling cycles in a collection of multidimensional heterogeneous time series data. In contrast to previous cycle modeling methods, CyHMMs deal with a number of challenges encountered in modeling real-world cycles: they can model multivariate data with discrete and continuous dimensions; they explicitly model and are robust to missing data; and they can share information across individuals to model variation both within and between individual time series. Experiments on synthetic and real-world health-tracking data demonstrate that CyHMMs infer cycle lengths more accurately than existing methods, with 58% lower error on simulated data and 63% lower error on real-world data compared to the best-performing baseline. CyHMMs can also perform functions which baselines cannot: they can model the progression of individual features/symptoms over the course of the cycle, identify the most variable features, and cluster individual time series into groups with distinct characteristics. Applying CyHMMs to two real-world health-tracking datasets -- of menstrual cycle symptoms and physical activity tracking data -- yields important insights including which symptoms to expect at each point during the cycle. We also find that people fall into several groups with distinct cycle patterns, and that these groups differ along dimensions not provided to the model. For example, by modeling missing data in the menstrual cycles dataset, we are able to discover a medically relevant group of birth control users even though information on birth control is not given to the model.Comment: Accepted at WWW 201

Generalized Species Sampling Priors with Latent Beta reinforcements

Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a {novel and probabilistically coherent family of non-exchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their theoretical clustering properties with those of the Dirichlet Process and the two parameters Poisson-Dirichlet process. The proposed construction provides a complete characterization of the joint process, differently from existing work. We then propose the use of such process as prior distribution in a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte Carlo sampler for posterior inference. We evaluate the performance of the prior and the robustness of the resulting inference in a simulation study, providing a comparison with popular Dirichlet Processes mixtures and Hidden Markov Models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array CGH data.Comment: For correspondence purposes, Edoardo M. Airoldi's email is [email protected]; Federico Bassetti's email is [email protected]; Michele Guindani's email is [email protected] ; Fabrizo Leisen's email is [email protected]. To appear in the Journal of the American Statistical Associatio

Nonparametric Bayesian Double Articulation Analyzer for Direct Language Acquisition from Continuous Speech Signals

Human infants can discover words directly from unsegmented speech signals without any explicitly labeled data. In this paper, we develop a novel machine learning method called nonparametric Bayesian double articulation analyzer (NPB-DAA) that can directly acquire language and acoustic models from observed continuous speech signals. For this purpose, we propose an integrative generative model that combines a language model and an acoustic model into a single generative model called the "hierarchical Dirichlet process hidden language model" (HDP-HLM). The HDP-HLM is obtained by extending the hierarchical Dirichlet process hidden semi-Markov model (HDP-HSMM) proposed by Johnson et al. An inference procedure for the HDP-HLM is derived using the blocked Gibbs sampler originally proposed for the HDP-HSMM. This procedure enables the simultaneous and direct inference of language and acoustic models from continuous speech signals. Based on the HDP-HLM and its inference procedure, we developed a novel double articulation analyzer. By assuming HDP-HLM as a generative model of observed time series data, and by inferring latent variables of the model, the method can analyze latent double articulation structure, i.e., hierarchically organized latent words and phonemes, of the data in an unsupervised manner. The novel unsupervised double articulation analyzer is called NPB-DAA. The NPB-DAA can automatically estimate double articulation structure embedded in speech signals. We also carried out two evaluation experiments using synthetic data and actual human continuous speech signals representing Japanese vowel sequences. In the word acquisition and phoneme categorization tasks, the NPB-DAA outperformed a conventional double articulation analyzer (DAA) and baseline automatic speech recognition system whose acoustic model was trained in a supervised manner.Comment: 15 pages, 7 figures, Draft submitted to IEEE Transactions on Autonomous Mental Development (TAMD

Substructure and Boundary Modeling for Continuous Action Recognition

This paper introduces a probabilistic graphical model for continuous action recognition with two novel components: substructure transition model and discriminative boundary model. The first component encodes the sparse and global temporal transition prior between action primitives in state-space model to handle the large spatial-temporal variations within an action class. The second component enforces the action duration constraint in a discriminative way to locate the transition boundaries between actions more accurately. The two components are integrated into a unified graphical structure to enable effective training and inference. Our comprehensive experimental results on both public and in-house datasets show that, with the capability to incorporate additional information that had not been explicitly or efficiently modeled by previous methods, our proposed algorithm achieved significantly improved performance for continuous action recognition.Comment: Detailed version of the CVPR 2012 paper. 15 pages, 6 figure