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 key difference between HSMMs and BOCPD is related with how inference is performed and its ultimate goal. HSMMs have been mostly used for batch processing of time series and retrospective inference of hidden states through the celebrated Forward-Backward and Viterbi algorithms @cite_2 . On the other hand, BOCPD focuses on the filtering setting (i.e., online updating) and on events which are relevant for the most recent observation. It does so by explicitly accounting for potentially incomplete segment realizations.
@cite_2
2753034091 2004469928 2096765155 2124271233
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. Hidden semi-Markov Model (HsMM) has been well studied and widely applied to many areas. The advantage of using an HsMM is its efficient forward-backward algorithm for estimating model parameters to best account for an observed sequence. In this paper, we propose an HsMM to model the distribution of network-wide traffic and use an observation window to distinguish DoS flooding attacks mixed within the normal background traffic. Several experiments are conducted to validate our method. Most current statistical natural language processing models use only local features so as to permit dynamic programming in inference, but this makes them unable to fully account for the long distance structure that is prevalent in language use. We show how to solve this dilemma with Gibbs sampling, a simple Monte Carlo method used to perform approximate inference in factored probabilistic models. By using simulated annealing in place of Viterbi decoding in sequence models such as HMMs, CMMs, and CRFs, it is possible to incorporate non-local structure while preserving tractable inference. We use this technique to augment an existing CRF-based information extraction system with long-distance dependency models, enforcing label consistency and extraction template consistency constraints. This technique results in an error reduction of up to 9 over state-of-the-art systems on two established information extraction tasks. Bayesian models provide powerful tools for analyzing complex time series data, but performing inference with large datasets is a challenge. Stochastic variational inference (SVI) provides a new framework for approximating model posteriors with only a small number of passes through the data, enabling such models to be fit at scale. However, its application to time series models has not been studied. In this paper we develop SVI algorithms for several common Bayesian time series models, namely the hidden Markov model (HMM), hidden semi-Markov model (HSMM), and the non-parametric HDP-HMM and HDP-HSMM. In addition, because HSMM inference can be expensive even in the minibatch setting of SVI, we develop fast approximate updates for HSMMs with durations distributions that are negative binomials or mixtures of negative binomials.