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用于时间序列建模与预测的贝叶斯上下文树状态空间模型AI 解读

A hierarchical Bayesian framework is introduced for developing tree-based mixture models for time series, partly motivated by applications in finance and forecasting. At the top level, meaningful discrete states are identified as appropriately quantised values of some of the most recent samples. At the bottom level, a different, arbitrary base model is associated with each state. This defines a very general framework that can be used in conjunction with any existing model…

利用贝叶斯上下文树检测离散数据变点并进行分段AI 解读

A new Bayesian modelling framework is introduced for piece-wise homogeneous variable-memory Markov chains, along with a collection of effective algorithmic tools for change-point detection and segmentation of discrete time series. Building on the recently introduced Bayesian Context Trees (BCT) framework, the distributions of different segments in a discrete time series are described as variable-memory Markov chains. Inference for the presence and location of change-points…

实值时间序列的上下文树加权：层级混合模型的贝叶斯推断AI 解读

Real-valued time series are ubiquitous in the sciences and engineering. In this work, a general, hierarchical Bayesian modelling framework is developed for building mixture models for times series. This development is based, in part, on the use of context trees, and it includes a collection of effective algorithmic tools for learning and inference. A discrete context (or 'state') is extracted for each sample, consisting of a discretised version of some of the most recent…

完全贝叶斯熵估计AI 解读

Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been developed for this task, typically based either on universal data compression algorithms, or on statistical estimators of the underlying process distribution. In this work, we propose a fully-Bayesian approach for entropy estimation.…

贝叶斯上下文树的后验表示：抽样、估计与收敛AI 解读

We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the induced posterior distribution on model space is derived in terms of a simple branching process, and several consequences of this are explored in theory and in practice. First, it is shown that the branching process representation leads to a…