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

2026-01-22

AI Summary

This work proposes a variational segmented binary tree model based on Bayesian context trees to address the challenges of flexibly modeling changepoint locations and achieving compact tree representations in time series segmentation. The method employs recursive logistic regression to dynamically characterize interval partitions over the time domain, jointly inferring both segmentation positions and tree depth. By integrating local variational approximation with the Context Tree Weighting (CTW) algorithm, the approach enables efficient posterior inference. Experimental results demonstrate that the model effectively recovers segmental structures in synthetic data while significantly enhancing the compactness and generalization capability of the resulting tree representation.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Segmentation

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• time series segmentation
• variable splitting
• Bayesian context tree
• interval partitioning
• binary tree models

Innovation

• Variable Splitting Binary Tree
• Bayesian Context Tree
• Time Series Segmentation
• Recursive Logistic Regression
• Context Tree Weighting