基于变分消息传递的贝叶斯函数主成分分析
Bayesian Functional Principal Components Analysis via Variational Message Passing
摘要：
函数型主成分分析是一种常用的函数型数据推理工具。标准方法依赖于平滑协方差表面的特征分解，以提取代表主要变化模式的正交函数。这种方法可能是一个计算密集型的过程，特别是在存在大型数据集的不规则观测。在本文中，我们开发了一种贝叶斯方法，其目的是直接确定Karhunen-Loève分解，而无需平滑和估计协方差曲面。更具体地说，我们开发了一个变分贝叶斯算法通过信息传递的因素图，这是更常见的称为变分信息传递。消息传递算法是划分层次统计模型中推理所需的代数和编码的强大工具。最近，有很多的重点制定变分推断算法的消息传递框架，因为它消除了需要重新推导近似后验密度函数，如果有一个变化的模型。相反，模型更改是通过更改因子图中的特定计算单元（称为片段）来处理的。我们扩展的概念变的消息传递功能的主成分分析。实际上，这是第一篇通过变分消息传递来解决函数式数据模型的文章。我们的方法引入了两个新的片段，是必要的贝叶斯函数主成分分析。我们提出的计算细节，一组模拟评估的准确性和速度，并应用到美国的温度数据。
英文摘要：
Functional principal components analysis is a popular tool for inference on functional data. Standard approaches rely on an eigendecomposition of a smoothed covariance surface in order to extract the orthonormal functions representing the major modes of variation. This approach can be a computationally intensive procedure, especially in the presence of large datasets with irregular observations. In this article, we develop a Bayesian approach, which aims to determine the Karhunen-Loève decomposition directly without the need to smooth and estimate a covariance surface. More specifically, we develop a variational Bayesian algorithm via message passing over a factor graph, which is more commonly referred to as variational message passing. Message passing algorithms are a powerful tool for compartmentalizing the algebra and coding required for inference in hierarchical statistical models. Recently, there has been much focus on formulating variational inference algorithms in the message passing framework because it removes the need for rederiving approximate posterior density functions if there is a change to the model. Instead, model changes are handled by changing specific computational units, known as fragments, within the factor graph. We extend the notion of variational message passing to functional principal components analysis. Indeed, this is the first article to address a functional data model via variational message passing. Our approach introduces two new fragments that are necessary for Bayesian functional principal components analysis. We present the computational details, a set of simulations for assessing accuracy and speed and an application to United States temperature data.
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。
