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.

翻译：本文提出了一种基于贝叶斯上下文树（BCT）模型的时间序列分割可变分裂二叉树（VSBT）模型。与先前BCT模型的应用不同，本模型中的树结构表示时间域上的区间划分。此外，区间划分通过递归逻辑回归模型表示。通过调整逻辑回归系数，本模型能够在每个区间内任意位置表示分裂点，从而实现更紧凑的树表示。为了同时估计分裂点位置与树深度，我们开发了一种有效的推断算法，该算法将逻辑回归的局部变分近似与上下文树加权（CTW）算法相结合。我们在合成数据上给出了数值示例，证明了本模型与算法的有效性。