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 observations preceding it. The set of all relevant contexts are represented as a discrete context-tree. At the bottom level, a different real-valued time series model is associated with each context-state, i.e., with each leaf of the tree. This defines a very general framework that can be used in conjunction with any existing model class to build flexible and interpretable mixture models. Extending the idea of context-tree weighting leads to algorithms that allow for efficient, exact Bayesian inference in this setting. The utility of the general framework is illustrated in detail when autoregressive (AR) models are used at the bottom level, resulting in a nonlinear AR mixture model. The associated methods are found to outperform several state-of-the-art techniques on simulated and real-world experiments.
Stable Global Weighting of Flow Mixtures using Simplex Exponential Moving Average
School of Computer Science and Informatics, Cardiff University（卡迪夫大学计算机科学与信息学学院）；Department of Computer Engineering, Turkish Air Force Academy, National Defence University（土耳其空军学院计算机工程系，国家防卫大学）
ADMIRE-BayesOpt: Accelerated Data MIxture RE-weighting for Language Models with Bayesian Optimization
Thomson Reuters Foundational Research & Imperial College London（汤姆逊·路透基础研究与帝国理工学院伦敦）；University of Virginia（弗吉尼亚大学）；Graphcore；Thomson Reuters Foundational Research（汤姆逊·路透基础研究）
A class of measure-valued Markov chains and Bayesian nonparametrics
自从（Math. Proc. Cambridge Philos.Soc.105（1989）579- 585）的开创性论文以来，测度值马尔可夫链引起了人们对贝叶斯非参数的兴趣，在该论文中引入了具有狄利克雷过程定律作为唯一不变测度的马尔可夫链。本文提出并研究了一类由可交换随机变量序列定义的测度值马尔可夫链。导出了这一新类的渐近性质，并讨论了与贝叶斯非参数混合模型和（Math. Proc. Cambridge Philos.Soc.105（1989）579- 585）提出的马尔可夫链的推广有关的应用。这些结果及其应用再次突出了贝叶斯非参数和测度值马尔可夫链理论之间的相互作用。
Inverse Problems for Partial Differential Equations with Jump Discontinuities in Coefficients via Two-Stage Physics-Informed Deep Learning and Statistical Mixture Models
School of Mathematics and Statistics（数学与统计学学院）；Northwestern Polytechnical University（西北工业大学）；Huazhong University of Science and Technology（华中科技大学）；Xiangtan University（湘潭大学）；Southern University of Science and Technology（南方科技大学）；MOE Key Laboratory for Complexity Science in Aerospace（航空航天复杂科学教育部重点实验室）；SandGold AI Research（SandGold AI研究院）
M$^3$TN: Multi-gate Mixture-of-Experts based Multi-valued Treatment Network for Uplift Modeling
Gaoling School of Artificial Intelligence, Renmin University of China（中国人民大学高瓴人工智能学院）；Beijing Key Laboratory of Big Data Management and Analysis Methods（北京大数据管理与分析方法重点实验室）
Functional Principal Component Analysis for Manifold-Indexed Data
The Institute for Data Innovation in Science, Seoul National University（首尔大学数据创新科学研究所）；Department of Statistics and School of Transdisciplinary Innovations, Seoul National University（首尔大学统计学院与跨学科创新学院）
