Continual Learning for Infinite Hierarchical Change-Point Detection

Abstract

Change-point detection (CPD) aims to locate abrupt transitions in the generative model of a sequence of observations. When Bayesian methods are considered, the standard practice is to infer the posterior distribution of the change-point locations. However, for complex models (high-dimensional or heterogeneous), it is not possible to perform reliable detection. To circumvent this problem, we propose to use a hierarchical model, which yields observations that belong to a lower-dimensional manifold. Concretely, we consider a latent-class model with an unbounded number of categories, which is based on the chinese-restaurant process (CRP). For this model we derive a continual learning mechanism that is based on the sequential construction of the CRP and the expectation-maximization (EM) algorithm with a stochastic maximization step. Our results show that the proposed method is able to recursively infer the number of underlying latent classes and perform CPD in a reliable manner.

Multinomial Sampling of Latent Variables for Hierarchical Change-Point Detection

“…This is understandable as the sampling methodology allows us to better characterize the latent variable distribution in that sections of the signal. Moreover, the infinite-dimensional approach of [10] which does not consider a fixed dimensionality for the latent space performs similar to our method. However, it does not detect small transitions in the shortlength scale of the time-series, as we do.…”

“…We remark that the true location of CPs is not provided. The methods considered for the comparison are i) the Bayesian CPD algorithm [1], ii) Hierarchical CPD [11], iii) the infinite-dimensional method of [10] and iv) the Multinomial-based approach proposed in this work. The detection curves are shown in Fig.…”

“…We illustrate an example on a human behavioral study, that detects changes in the circadian patterns of a user. In future work, this could be integrated with other CPD methods that consider the dimensionality of the latent variables unbounded [10].…”

“…Moreover, we would like to perform CP detection over the true sequence of assignments z 1∶t , but we cannot observe them. Instead, we only know the sequence of posterior distributions p(z 1∶t |x 1∶t ) that has been previously inferred via, for instance, the online expectation-maximization (EM) algorithm [5] or other continual learning strategies [10]. As the chosen approach, we consider to use maximum a-posteriori (MAP) estimates of the latent variables z t as our pseudoobservations.…”

“…The last step is to obtain the complete sequence of posterior estimates p(z 1∶t |x 1∶t ) via the EM algorithm. The learning method of the mixture model can be adapted to the online nature of CPD using [5] or [10] if the number of classes K is unbounded. Results obtained are shown in Fig.…”