Dirichlet Process Hidden Markov Model Research Articles

Towards Attack Detection in Multimodal Cyber-Physical Systems with Sticky HDP-HMM based Time Series Analysis

Automatic detection of the precise occurrence and duration of an attack reflected in time-series logs generated by cyber-physical systems is a challenging problem. This problem is exacerbated when performing this analysis using logs with limited system information. In a realistic scenario, multiple and differing attack methods may be employed in rapid succession. Modern or legacy systems operate in multiple modes and contain multiple devices recording a variety of continuous and categorical data streams. This work presents a non-parametric Bayesian framework that addresses these challenges using the sticky Hierarchical Dirichlet Process Hidden Markov Model (sHDP-HMM) . Additionally, we explore metrics for measuring the accuracy of the detected events, their timings and durations, and compare the computational efficiency of different inference implementations of the model. The efficacy of attack detection is demonstrated in two settings: an avionics testbed and a consumer robot.

Forecasting-Aided Joint Topology/State Estimation for Distribution Systems via Bayesian Non-Parametric Modeling

To ensure the validity of distribution system state estimation (DSSE) in case of frequent topology changes, it is important to develop DSSE methods with topology identification capability. This paper proposes a forecasting-aided joint topology/state estimation method for distribution systems considering topology changes. The joint estimation problem is formulated under the Dirichlet-process hidden-Markov-model (DP-HMM), which requires establishing state-space models for a partial set of topologies (i.e., predefined topologies) and constructing probability distribution of the other possible topologies (i.e., unseen topologies). A particle filter (PF)-based method is proposed to resolve this joint estimation problem, which augments the particles to include both topology-related variables and nodal voltages. Its robustness against measurement outliers is enhanced by adopting the anti-zero bias modification. The base distribution for unseen topologies are constructed via probabilistic neural networks (PNNs). To improve the accuracy of PNNs, the synthetic minority oversampling technique is employed to rebalance the training data. Aiming at efficiency enhancement, a rule-based candidate set reduction method is proposed for the unseen topologies to improve topology sampling validity. Test results on the IEEE 33-bus, IEEE 123-bus, and a modified 2516-bus distribution systems show that the proposed method has good state and topology estimation accuracy while achieving good scalability.

A Bayesian Nonparametric Latent Space Approach to Modeling Evolving Communities in Dynamic Networks

The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for clustering with this approach exist for dynamic networks, they all assume a static community structure. This paper presents a Bayesian nonparametric model for dynamic networks that can model networks with evolving community structures. Our model extends existing latent space approaches by explicitly modeling the additions, deletions, splits, and mergers of groups with a hierarchical Dirichlet process hidden Markov model. Our proposed approach, the hierarchical Dirichlet process latent position cluster model (HDP-LPCM), incorporates transitivity, models both individual and group level aspects of the data, and avoids the computationally expensive selection of the number of groups required by most popular methods. We provide a Markov chain Monte Carlo estimation algorithm and demonstrate its ability to detect evolving community structure in a network of military alliances during the Cold War and a narrative network constructed from the Game of Thrones television series.

Extracting Overtaking Segments by Unsupervised Clustering and Predicting Nonmotorized Vehicle’s Trajectory

Interpretation of flexible cycling behavior has always been a tough task. It is meaningful to understand the overtaking behavior of cyclists for its threats to safety and its high frequency on shared roads. Advanced unsupervised nonparametric clustering methods are compared to distinguish the overtaking segments from the whole trajectory based on the cycling characteristics of nonmotorized two-wheelers, while the hierarchical Dirichlet process hidden Markov model (HDPHMM) outperforms the mixture model via the Dirichlet process (DP mixture model) and topic model via the hierarchical Dirichlet process (HDP topic model). HDPHMM clusters each record into different states and results in more continuous segments. Based on marked vehicle types, which state of clustering model represents the overtaking condition is deduced. The overtaking segments resulted from HDPHMM show the highest homogeneity in cycling features with actual overtaking behavior. Another practical task is to predict the overtaking trajectory and respond to overtaking behavior in advance. Comparing original trajectory and subdivided trajectory, it is found that training model with grouped data, which have homogeneous features, can improve prediction accuracy. With enough trainable samples, CNN + LSTM hybrid structure can achieve trajectory prediction with a mean absolute error of 3 cm. The segmentation produces trajectory segments with similar characteristics. The model is trained with overtaking trajectory segments. With tens of times less trainable data, the prediction on overtaking trajectory still keeps a mean absolute error of about 5 cm. Subdividing trajectory into segments with homogeneous features can improve the prediction accuracy and reduce the requirement of trainable data volume.

Multitaper Infinite Hidden Markov Model for EEG.

Electroencephalographam (EEG) monitoring of neural activity is widely used for identifying underlying brain states. For inference of brain states, researchers have often used Hidden Markov Models (HMM) with a fixed number of hidden states and an observation model linking the temporal dynamics embedded in EEG to the hidden states. The use of fixed states may be limiting, in that 1) pre-defined states might not capture the heterogeneous neural dynamics across individuals and 2) the oscillatory dynamics of the neural activity are not directly modeled. To this end, we use a Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM), which discovers the set of hidden states that best describes the EEG data, without a-priori specification of state number. In addition, we introduce an observation model based on classical asymptotic results of frequency domain properties of stationary time series, along with the description of the conditional distributions for Gibbs sampler inference. We then combine this with multitaper spectral estimation to reduce the variance of the spectral estimates. By applying our method to simulated data inspired by sleep EEG, we arrive at two main results: 1) the algorithm faithfully recovers the spectral characteristics of the true states, as well as the right number of states and 2) the incorporation of the multitaper framework produces a more stable estimate than traditional periodogram spectral estimates.

Integrating Driving Behavior and Traffic Context Through Signal Symbolization for Data Reduction and Risky Lane Change Detection

A novel method for integrating driving behavior and traffic context through signal symbolization is presented in this paper. This symbolization framework is proposed as a data reduction method for naturalistic driving studies. Continuous sensor signals have been converted and reduced into sequences of symbols (chunks) using a sticky hierarchical Dirichlet process hidden Markov model and a nested Pitman–Yor language model. Then, co-occurrence chunking (COOC), the proposed integration method, has been applied to the driver behavior and the traffic context chunks. After the integration, COOC chunks have been associated with prototype driving scenes by using latent Dirichlet allocation. Finally, the translated sequence of chunks has been clustered into groups. Risky lane change detection experiments have been conducted with the symbolized data for evaluation purposes. A dataset comprised of 988 lane change scenes has been utilized for this process. Co-occurrence chunking with clustering provided the best risky lane change detection.

Extracting Traffic Primitives Directly From Naturalistically Logged Data for Self-Driving Applications

Developing an automated vehicle, that can handle complicated driving scenarios and appropriately interact with other road users, requires the ability to semantically learn and understand driving environment, oftentimes, based on analyzing massive amounts of naturalistic driving data. An important paradigm that allows automated vehicles to both learn from human drivers and gain insights is understanding the principal compositions of the entire traffic, termed as traffic primitives. However, the exploding data growth presents a great challenge in extracting primitives from high-dimensional time-series traffic data with various types of road users engaged. Therefore, automatically extracting primitives is becoming one of the cost-efficient ways to help autonomous vehicles understand and predict the complex traffic scenarios. In addition, the extracted primitives from raw data should 1) be appropriate for automated driving applications and also 2) be easily used to generate new traffic scenarios. However, existing literature does not provide a method to automatically learn these primitives from large-scale traffic data. The contribution of this paper has two manifolds. The first one is that we proposed a new framework to generate new traffic scenarios from a handful of limited traffic data. The second one is that we introduce a nonparametric Bayesian learning method -- a sticky hierarchical Dirichlet process hidden Markov model -- to automatically extract primitives from multidimensional traffic data without prior knowledge of the primitive settings. The developed method is then validated using one day of naturalistic driving data. Experiment results show that the nonparametric Bayesian learning method is able to extract primitives from traffic scenarios where both the binary and continuous events coexist.

Statistical Anomaly Detection in Human Dynamics Monitoring Using a Hierarchical Dirichlet Process Hidden Markov Model

Understanding of human dynamics has drawn attention to various areas. The wide spread of positioning technologies, such as GPS facilitates location information to be obtained with high spatio-temporal resolution as well as at low costs. By collecting individual location information in real time, monitoring of human dynamics has recently become possible and is expected to the area of dynamic traffic control. In this monitoring, detecting anomalous states of human dynamics become important. This research aims to define an anomaly detection problem of the human dynamics monitoring with time-series gridded population data and develop an anomaly detection method for this problem. According to the result of a review we have conducted, we discussed the characteristics of the anomaly detection in human dynamics monitoring and categorized our problem to a semi-supervised anomaly detection problem that detects contextual anomalies behind time-series data. We developed an anomaly detection method based on a sticky hierarchical Dirichlet process hidden Markov model, which is able to estimate the number of latent states according to the input data. Results of the experiment with synthetic data showed that our proposed method has good fundamental performance with respect to the detection rate. Through the experiments with real gridded population data, anomalies were detected when and where an actual social event had occurred.

Dual Sticky Hierarchical Dirichlet Process Hidden Markov Model and Its Application to Natural Language Description of Motions.

In this paper, a new nonparametric Bayesian model called the dual sticky hierarchical Dirichlet process hidden Markov model (HDP-HMM) is proposed for mining activities from a collection of time series data such as trajectories. All the time series data are clustered. Each cluster of time series data, corresponding to a motion pattern, is modeled by an HMM. Our model postulates a set of HMMs that share a common set of states (topics in an analogy with topic models for document processing), but have unique transition distributions. The number of HMMs and the number of topics are both automatically determined. The sticky prior avoids redundant states and makes our HDP-HMM more effective to model multimodal observations. For the application to motion trajectory modeling, topics correspond to motion activities. The learnt topics are clustered into atomic activities which are assigned predicates. We propose a Bayesian inference method to decompose a given trajectory into a sequence of atomic activities. The sources and sinks in the scene are learnt by clustering endpoints (origins and destinations) of trajectories. The semantic motion regions are learnt using the points in trajectories. On combining the learnt sources and sinks, the learnt semantic motion regions, and the learnt sequence of atomic activities, the action represented by a trajectory can be described in natural language in as automatic a way as possible. The effectiveness of our dual sticky HDP-HMM is validated on several trajectory datasets. The effectiveness of the natural language descriptions for motions is demonstrated on the vehicle trajectories extracted from a traffic scene.

A Doubly Hierarchical Dirichlet Process Hidden Markov Model with a Non-Ergodic Structure

Nonparametric Bayesian models use a Bayesian framework to learn model complexity automatically from the data, eliminating the need for a complex model selection process. A Hierarchical Dirichlet Process Hidden Markov Model (HDPHMM) is the nonparametric Bayesian equivalent of a hidden Markov model (HMM), but is restricted to an ergodic topology that uses a Dirichlet Process Model to achieve a mixture distribution-like model. For applications involving ordered sequences (e.g., speech recognition), it is desirable to impose a left-to-right structure on the model. In this paper, we introduce a model based on HDPHMM that: 1) shares data points between states, 2) models non-ergodic structures, and 3) models non-emitting states. The first point is particularly important because Gaussian mixture models, which support such sharing, have been very effective at modeling modalities in a signal (e.g., speaker variability). Further, sharing data points allows models to be estimated more accurately, an important consideration for applications such as speech recognition in which some mixture components occur infrequently. We demonstrate that this new model produces a 20% relative reduction in error rate for phoneme classification and an 18% relative reduction on a speech recognition task on the TIMIT Corpus compared to a baseline system consisting of a parametric HMM.

Dirichlet Process Hidden Markov Multiple Change-point Model

This paper proposes a new Bayesian multiple change-point model which is based on the hidden Markov approach. The Dirichlet process hidden Markov model does not require the specification of the number of change-points a priori. Hence our model is robust to model specification in contrast to the fully parametric Bayesian model. We propose a general Markov chain Monte Carlo algorithm which only needs to sample the states around change-points. Simulations for a normal mean-shift model with known and unknown variance demonstrate advantages of our approach. Two applications, namely the coal-mining disaster data and the real United States Gross Domestic Product growth, are provided. We detect a single change-point for both the disaster data and US GDP growth. All the change-point locations and posterior inferences of the two applications are in line with existing methods.

Inertial Hidden Markov Models: Modeling Change in Multivariate Time Series

Faced with the problem of characterizing systematic changes in multivariate time series in an unsupervised manner, we derive and test two methods of regularizing hidden Markov models for this task. Regularization on state transitions provides smooth transitioning among states, such that the sequences are split into broad, contiguous segments. Our methods are compared with a recent hierarchical Dirichlet process hidden Markov model (HDP-HMM) and a baseline standard hidden Markov model, of which the former suffers from poor performance on moderate-dimensional data and sensitivity to parameter settings, while the latter suffers from rapid state transitioning, over-segmentation and poor performance on a segmentation task involving human activity accelerometer data from the UCI Repository. The regularized methods developed here are able to perfectly characterize change of behavior in the human activity data for roughly half of the real-data test cases, with accuracy of 94% and low variation of information. In contrast to the HDP-HMM, our methods provide simple, drop-in replacements for standard hidden Markov model update rules, allowing standard expectation maximization (EM) algorithms to be used for learning.

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-Markov modeling, which has been developed mainly in the parametric non-Bayesian 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.

Inference of temporally varying Bayesian networks.

Motivation: When analysing gene expression time series data, an often overlooked but crucial aspect of the model is that the regulatory network structure may change over time. Although some approaches have addressed this problem previously in the literature, many are not well suited to the sequential nature of the data.Results: Here, we present a method that allows us to infer regulatory network structures that may vary between time points, using a set of hidden states that describe the network structure at a given time point. To model the distribution of the hidden states, we have applied the Hierarchical Dirichlet Process Hidden Markov Model, a non-parametric extension of the traditional Hidden Markov Model, which does not require us to fix the number of hidden states in advance. We apply our method to existing microarray expression data as well as demonstrating is efficacy on simulated test data.Contact: thomas.thorne@imperial.ac.uk

A sticky HDP-HMM with application to speaker diarization

We consider the problem of speaker diarization, the problem of segmenting an audio recording of a meeting into temporal segments corresponding to individual speakers. The problem is rendered particularly difficult by the fact that we are not allowed to assume knowledge of the number of people participating in the meeting. To address this problem, we take a Bayesian nonparametric approach to speaker diarization that builds on the hierarchical Dirichlet process hidden Markov model (HDP-HMM) of Teh et al. [J. Amer. Statist. Assoc. 101 (2006) 1566–1581]. Although the basic HDP-HMM tends to over-segment the audio data—creating redundant states and rapidly switching among them—we describe an augmented HDP-HMM that provides effective control over the switching rate. We also show that this augmentation makes it possible to treat emission distributions nonparametrically. To scale the resulting architecture to realistic diarization problems, we develop a sampling algorithm that employs a truncated approximation of the Dirichlet process to jointly resample the full state sequence, greatly improving mixing rates. Working with a benchmark NIST data set, we show that our Bayesian nonparametric architecture yields state-of-the-art speaker diarization results.

Music Analysis Using Hidden Markov Mixture Models

We develop a hidden Markov mixture model based on a Dirichlet process (DP) prior, for representation of the statistics of sequential data for which a single hidden Markov model (HMM) may not be sufficient. The DP prior has an intrinsic clustering property that encourages parameter sharing, and this naturally reveals the proper number of mixture components. The evaluation of posterior distributions for all model parameters is achieved in two ways: 1) via a rigorous Markov chain Monte Carlo method; and 2) approximately and efficiently via a variational Bayes formulation. Using DP HMM mixture models in a Bayesian setting, we propose a novel scheme for music analysis, highlighting the effectiveness of the DP HMM mixture model. Music is treated as a time-series data sequence and each music piece is represented as a mixture of HMMs. We approximate the similarity of two music pieces by computing the distance between the associated HMM mixtures. Experimental results are presented for synthesized sequential data and from classical music clips. Music similarities computed using DP HMM mixture modeling are compared to those computed from Gaussian mixture modeling, for which the mixture modeling is also performed using DP. The results show that the performance of DP HMM mixture modeling exceeds that of the DP Gaussian mixture modeling.