用于后验近似的贝叶斯希尔伯特空间
Bayes Hilbert Spaces for Posterior Approximation
AI总结：
本文研究将贝叶斯希尔伯特空间应用于后验近似问题，建立其与贝叶斯核心集算法及核距离之间的新联系，为大规模数据下的贝叶斯计算提供理论基础。
摘要：
在贝叶斯模型中执行推断需要采样算法从后验分布中抽取样本。随着数据集规模的增大，这一过程的计算代价变得极其高昂。构造评估成本低廉的后验近似是规避该问题的常用方法。这引出一个问题：什么才是进行贝叶斯后验测度近似的合适空间？本文研究贝叶斯希尔伯特空间在后验近似问题中的应用。贝叶斯希尔伯特空间在函数型数据分析中用于处理观测函数为概率密度函数的情形，其在计算贝叶斯问题中的应用尚处于起步阶段。本文将概述贝叶斯希尔伯特空间及其与贝叶斯计算的关联，特别是贝叶斯希尔伯特空间、贝叶斯核心集算法与基于核的距离之间的新联系。
英文摘要：
Performing inference in Bayesian models requires sampling algorithms to draw samples from the posterior. This becomes prohibitively expensive as the size of data sets increase. Constructing approximations to the posterior which are cheap to evaluate is a popular approach to circumvent this issue. This begs the question of what is an appropriate space to perform approximation of Bayesian posterior measures. This manuscript studies the application of Bayes Hilbert spaces to the posterior approximation problem. Bayes Hilbert spaces are studied in functional data analysis in the context where observed functions are probability density functions and their application to computational Bayesian problems is in its infancy. This manuscript shall outline Bayes Hilbert spaces and their connection to Bayesian computation, in particular novel connections between Bayes Hilbert spaces, Bayesian coreset algorithms and kernel-based distances.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
