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
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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.