Soft Bayesian Context Tree Models for Real-Valued Time Series

2026-01-16

AI Summary

This work proposes Soft-Bayesian Context Trees (Soft-BCT), a novel extension of Bayesian context trees (BCT) for real-valued time series modeling. Addressing the limitations of existing BCT models—which rely on hard partitioning and thus constrain expressive capacity—the proposed method introduces, for the first time, a probabilistic soft partitioning mechanism into the BCT framework to more flexibly capture contextual dependencies. An efficient learning algorithm based on variational inference is developed to jointly optimize both the soft partitions and the tree structure. Experimental evaluations on multiple real-world datasets demonstrate that Soft-BCT achieves modeling performance on par with or superior to current state-of-the-art approaches, thereby validating its effectiveness and advantages in capturing complex temporal structures.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• 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

Abstract

This paper proposes the soft Bayesian context tree model (Soft-BCT), which is a novel BCT model for real-valued time series. The Soft-BCT considers soft (probabilistic) splits of the context space, instead of hard (deterministic) splits of the context space as in the previous BCT for real-valued time series. A learning algorithm of the Soft-BCT is proposed based on the variational inference. For some real-world datasets, the Soft-BCT demonstrates almost the same or superior performance to the previous BCT.

Problem

• Bayesian context tree
• real-valued time series
• soft splits
• context space partitioning
• probabilistic modeling

Innovation

• Soft Bayesian Context Tree
• soft splits
• variational inference
• real-valued time series
• probabilistic modeling