Bayesian Nonparametric Inference of Switching Linear Dynamical Systems

Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector autoregressive (VAR) process. Our Bayesian nonparametric approach utilizes a hierarchical Dirichlet process prior to learn an unknown number of persistent, smooth dynamical modes. We additionally employ automatic relevance determination to infer a sparse set of dynamic dependencies allowing us to learn SLDS with varying state dimension or switching VAR processes with varying autoregressive order. We develop a sampling algorithm that combines a truncated approximation to the Dirichlet process with efficient joint sampling of the mode and state sequences. The utility and flexibility of our model are demonstrated on synthetic data, sequences of dancing honey bees, the IBOVESPA stock index, and a maneuvering target tracking application.Comment: 50 pages, 7 figure

Dynamic Hierarchical Dirichlet Process for Abnormal Behaviour Detection in Video

This paper proposes a novel dynamic Hierarchical Dirichlet Process topic model that considers the dependence between successive observations. Conventional posterior inference algorithms for this kind of models require processing of the whole data through several passes. It is computationally intractable for massive or sequential data. We design the batch and online inference, based on the Gibbs sampling, for our model. It allows to process sequential data, incrementally updating the model by a new observation. The model is applied to abnormal behaviour detection in video sequences. A new abnormality measure is proposed for decision making. The proposed method is compared with the method based on the non-dynamic Hierarchical Dirichlet Process, for which we also derive the online Gibbs sampler and the abnormality measure. The experimental results show that the consideration of the dynamics in a topic model improves the classification performance for abnormal behaviour detection

A Stochastic Hybrid Framework for Driver Behavior Modeling Based on Hierarchical Dirichlet Process

Scalability is one of the major issues for real-world Vehicle-to-Vehicle network realization. To tackle this challenge, a stochastic hybrid modeling framework based on a non-parametric Bayesian inference method, i.e., hierarchical Dirichlet process (HDP), is investigated in this paper. This framework is able to jointly model driver/vehicle behavior through forecasting the vehicle dynamical time-series. This modeling framework could be merged with the notion of model-based information networking, which is recently proposed in the vehicular literature, to overcome the scalability challenges in dense vehicular networks via broadcasting the behavioral models instead of raw information dissemination. This modeling approach has been applied on several scenarios from the realistic Safety Pilot Model Deployment (SPMD) driving data set and the results show a higher performance of this model in comparison with the zero-hold method as the baseline.Comment: This is the accepted version of the paper in 2018 IEEE 88th Vehicular Technology Conference (VTC2018-Fall) (references added, title and abstract modified

Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments

Optical microscopy provides rich spatio-temporal information characterizing in vivo molecular motion. However, effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state changes, e.g., changes induced by dynamic micro-environments, photobleaching, and other heterogeneity inherent in biological processes. This study focuses on techniques for analyzing Single Particle Tracking (SPT) data experiencing abrupt state changes. We demonstrate the approach on GFP tagged chromatids experiencing metaphase in yeast cells and probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes are induced by factors such as microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, etc. Simulations are used to demonstrate the relevance of the approach in more general SPT data analyses. Refined force estimates are obtained by adopting and modifying a nonparametric Bayesian modeling technique, the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT applications. The HDP-SLDS method shows promise in systematically identifying dynamical regime changes induced by unobserved state changes when the number of underlying states is unknown in advance (a common problem in SPT applications). We expand on the relevance of the HDP-SLDS approach, review the relevant background of Hierarchical Dirichlet Processes, show how to map discrete time HDP-SLDS models to classic SPT models, and discuss limitations of the approach. In addition, we demonstrate new computational techniques for tuning hyperparameters and for checking the statistical consistency of model assumptions directly against individual experimental trajectories; the techniques circumvent the need for "ground-truth" and subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One publication available freely as an open-access article at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763

Modeling Topic and Role Information in Meetings using the Hierarchical Dirichlet Process

Abstract. In this paper, we address the modeling of topic and role information in multiparty meetings, via a nonparametric Bayesian model called the hierarchical Dirichlet process. This model provides a powerful solution to topic modeling and a flexible framework for the incorporation of other cues such as speaker role information. We present our modeling framework for topic and role on the AMI Meeting Corpus, and illustrate the effectiveness of the approach in the context of adapting a baseline language model in a large-vocabulary automatic speech recognition system for multiparty meetings. The adapted LM produces significant improvements in terms of both perplexity and word error rate.