论文检索

贝叶斯学习中的经验贝叶斯：理解一种常见实践AI 解读

In applications of Bayesian procedures, once a class of priors has been chosen, it may be tempting to fix the prior's hyperparameters from the data, in an empirical Bayes (EB) fashion, usually by their maximum marginal likelihood estimates (MMLE). This is a quite common but questionable practice, lacking a rigorous theoretical basis. We provide a theoretical framework where this form of EB is regarded as a computational strategy for approximating a genuine Bayesian posterior…

预印本版本摘要 · 查看来源

混合模型序贯学习程序的拟贝叶斯性质AI 解读

Summary Bayesian methods are often optimal, yet increasing pressure for fast computations, especially with streaming data, brings renewed interest in faster, possibly suboptimal, solutions. The extent to which these algorithms approximate Bayesian solutions is a question of interest, but often unanswered. We propose a methodology to address this question in predictive settings, when the algorithm can be reinterpreted as a probabilistic predictive rule. We specifically…

函数型数据的混合式 Dirichlet 混合模型AI 解读

Summary In functional data analysis, curves or surfaces are observed, up to measurement error, at a finite set of locations, for, say, a sample of n individuals. Often, the curves are homogeneous, except perhaps for individual-specific regions that provide heterogeneous behaviour (e.g. ‘damaged’ areas of irregular shape on an otherwise smooth surface). Motivated by applications with functional data of this nature, we propose a Bayesian mixture model, with the aim of…

伯恩斯坦多项式后验的一致性AI 解读

Summary A Bernstein prior is a probability measure on the space of all the distribution functions on [0, 1]. Under very general assumptions, it selects absolutely continuous distribution functions, whose densities are mixtures of known beta densities. The Bernstein prior is of interest in Bayesian nonparametric inference with continuous data. We study the consistency of the posterior from a Bernstein prior. We first show that, under mild assumptions, the posterior is weakly…