用贝叶斯上下文树构建时间序列分割的可变区间二叉树模型。
Variable Splitting Binary Tree Models Based on Bayesian Context Tree Models for Time Series Segmentation
- 通过递归逻辑回归实现时间区间任意位置的分裂点建模。
- 结合变分近似与上下文树加权算法，同步估计分裂点与树深度。
- 适用于需要精细时间段划分的时序分析任务。
我们提出一种基于贝叶斯上下文树（BCT）模型的可变区间二叉树（VSBT）模型，用于时间序列分割。与以往应用不同，本模型中的树结构表示时间域上的区间划分，且区间划分由递归逻辑回归模型刻画。通过调整逻辑回归系数，模型可在每个区间内任意位置表示分裂点，从而实现更紧凑的树结构表示。为同时估计分裂点位置与树深度，我们设计了一种有效推断算法，结合局部变分近似与上下文树加权（CTW）算法。在合成数据上的数值实验验证了该模型与算法的有效性。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。