Variable Splitting Binary Tree Models Based on Bayesian Context Tree Models for Time Series Segmentation

TL;DR

This paper introduces a novel Bayesian context tree-based variable splitting binary tree model for time series segmentation, utilizing recursive logistic regression for flexible interval partitioning and an efficient inference algorithm.

Contribution

The paper presents a new VSBT model that improves time series segmentation by flexible interval partitioning and a combined inference algorithm for split position and tree depth estimation.

Findings

Effective segmentation demonstrated on synthetic data.

Flexible split positioning within intervals.

Compact tree representations achieved.

Abstract

We propose a variable splitting binary tree (VSBT) model based on Bayesian context tree (BCT) models for time series segmentation. Unlike previous applications of BCT models, the tree structure in our model represents interval partitioning on the time domain. Moreover, interval partitioning is represented by recursive logistic regression models. By adjusting logistic regression coefficients, our model can represent split positions at arbitrary locations within each interval. This enables more compact tree representations. For simultaneous estimation of both split positions and tree depth, we develop an effective inference algorithm that combines local variational approximation for logistic regression with the context tree weighting (CTW) algorithm. We present numerical examples on synthetic data demonstrating the effectiveness of our model and algorithm.