Online detection of instantaneous changes in the generative process of a data sequence generally focuses on retrospective inference of such change points without considering their future occurrences. We extend the Bayesian Online Change Point Detection algorithm to also infer the number of time steps until the next change point (i.e., the residual time). This enables us to handle observation models which depend on the total segment duration, which is useful to model data sequences with temporal scaling. In addition, we extend the model by removing the i.i.d. assumption on the observation model parameters. The resulting inference algorithm for segment detection can be deployed in an online fashion, and we illustrate applications to synthetic and to two medical real-world data sets.
The segmentation and classification of time series has many applications in different fields such as predicting failures in an oil process plant, reconstructing trajectories in air traffic control, the identification of interaction scenarios in robotic environments, real-time brain computer interfaces, probabilistic forecasting of volcano eruptions or forecasting time series with multiple seasonal patterns . For a recent review of change point detection methods we refer to . These models have been especially popular in computer vision for human motion modeling . Regarding the modeling aspect, Gaussian processes have been used to model temporal structure within segments @cite_0 . Alternative methods, which are often based on HMMs, have recently been combined with recurrent and structured inference procedures . In the following, we provide more details about the models we are building on top of: HSMMs and BOCPD, and we point out the differences concerning inference and comment on a setting which leads to a similar generative model.
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Segmentation and labeling of high dimensional time series data has wide applications in behavior understanding and medical diagnosis. Due to the difficulty in obtaining the label information for high dimensional data, realizing this objective in an unsupervised way is highly desirable. Hidden Semi-Markov Model (HSMM) is a classical tool for this problem. However, existing HSMM and its variants has simple conditional assumptions of observations, thus the ability to capture the nonlinear and complex dynamics within segments is limited. To tackle this limitation, we propose to incorporate the Recurrent Neural Network (RNN) to model the generative process in HSMM, resulting the Recurrent HSMM (R-HSMM). To accelerate the inference while preserving accuracy, we designed a structure encoding function to mimic the exact inference. By generalizing the penalty method to distribution space, we are able to train the model and the encoding function simultaneously. Empirical results show that the proposed R-HSMM achieves the state-of-the-art performances on both synthetic and real-world datasets. We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our model discovers a latent set of dynamical behaviors shared among the sequences, and segments each time series into regions defined by a subset of these behaviors. Using a beta process prior, the size of the behavior set and the sharing pattern are both inferred from data. We develop Markov chain Monte Carlo (MCMC) methods based on the Indian buffet process representation of the predictive distribution of the beta process. Our MCMC inference algorithm efficiently adds and removes behaviors via novel split-merge moves as well as data-driven birth and death proposals, avoiding the need to consider a truncated model. We demonstrate promising results on unsupervised segmentation of human motion capture data. 1. Introduction. Classical time series analysis has generally focused on the study of a single (potentially multivariate) time series. Instead, we consider analyzing collections of related time series, motivated by the increasing abundance of such data in many domains. In this work we explore this problem by considering time series produced by motion capture sensors on the joints of people performing exercise routines. An individual recording provides a multivariate time series that can be segmented into types of exercises (e.g., jumping jacks, arm-circles, and twists). Each exercise type describes locally coherent and simple dynamics that persist over a segment of time. We have such motion capture recordings from multiple individuals, each of whom performs some subset of a global set of exercises, as shown in Figure1. Our goal is to discover the set of global exercise types (“behaviors”) and their occurrences in each individual’s data stream. We would like to take advantage of the overlap between individuals: if a jumping-jack behavior is discovered in one sequence, then it can be used to model data for other individuals. In the past few years there has been increased interest in using data-mining techniques to extract interesting patterns from time series data generated by sensors monitoring temporally varying phenomenon. Most work has assumed that raw data is somehow processed to generate a sequence of events, which is then mined for interesting episodes. In some cases the rule for determining when a sensor reading should generate an event is well known. However, if the phenomenon is ill-understood, stating such a rule is difficult. Detection of events in such an environment is the focus of this paper. Consider a dynamic phenomenon whose behavior changes enough over time to be considered a qualitatively significant change. The problem we investigate is of identifying the time points at which the behavior change occurs. In the statistics literature this has been called the change-point detection problem. The standard approach has been to (a) upriori determine the number of change-points that are to be discovered, and (b) decide the function that will be used for curve fitting in the interval between successive change-points. In this paper we generalize along both these dimensions. We propose an iterative algorithm that fits a model to a time segment, and uses a likelihood criterion to determine if the segment should be partitioned further, i.e. if it contains a new changepoint. In this paper we present algorithms for both the batch and incremental versions of the problem, and evaluate their behavior with synthetic and real data. Finally, we present initial results comparing the change-points detected by the batch algorithm with those detected by people using visual inspection. In this paper we present a Bayesian framework for parsing images into their constituent visual patterns. The parsing algorithm optimizes the posterior probability and outputs a scene representation as a "parsing graph", in a spirit similar to parsing sentences in speech and natural language. The algorithm constructs the parsing graph and re-configures it dynamically using a set of moves, which are mostly reversible Markov chain jumps. This computational framework integrates two popular inference approaches--generative (top-down) methods and discriminative (bottom-up) methods. The former formulates the posterior probability in terms of generative models for images defined by likelihood functions and priors. The latter computes discriminative probabilities based on a sequence (cascade) of bottom-up tests filters. In our Markov chain algorithm design, the posterior probability, defined by the generative models, is the invariant (target) probability for the Markov chain, and the discriminative probabilities are used to construct proposal probabilities to drive the Markov chain. Intuitively, the bottom-up discriminative probabilities activate top-down generative models. In this paper, we focus on two types of visual patterns--generic visual patterns, such as texture and shading, and object patterns including human faces and text. These types of patterns compete and cooperate to explain the image and so image parsing unifies image segmentation, object detection, and recognition (if we use generic visual patterns only then image parsing will correspond to image segmentation (Tu and Zhu, 2002. IEEE Trans. PAMI, 24(5):657--673). We illustrate our algorithm on natural images of complex city scenes and show examples where image segmentation can be improved by allowing object specific knowledge to disambiguate low-level segmentation cues, and conversely where object detection can be improved by using generic visual patterns to explain away shadows and occlusions.