Continual Learning for Infinite Hierarchical Change-Point Detection
This addresses the challenge of change-point detection in complex data for applications like signal processing or time-series analysis, representing an incremental improvement through a novel hierarchical approach.
The paper tackles the problem of reliable change-point detection in complex, high-dimensional models by proposing a hierarchical latent-class model with an unbounded number of categories based on the Chinese-restaurant process. The result is a continual learning mechanism that recursively infers latent classes and performs detection reliably.
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.