论文标题
关于使用多元$ t $分布的强大概率主成分分析
On Robust Probabilistic Principal Component Analysis using Multivariate $t$-Distributions
论文作者
论文摘要
概率主成分分析（PPCA）是高斯潜在变量模型的框架下主成分分析（PCA）的概率重新印象。为了提高PPCA的鲁棒性，已提议将基本的高斯分布更改为多元分布。基于$ t $分布作为高斯分布的比例混合物的表示，使用层次模型进行实施。但是，在现有文献中，实施的层次模型并不能产生同等的解释。 在本文中，我们介绍了高级多元$ t $ -PPCA框架与用于实现的层次模型之间的两组等效关系。在这样做的过程中，我们通过指定正确的对应关系来阐明文献中当前的虚假陈述。此外，我们在理论和仿真研究中讨论了不同多元$ t $ robust PPCA方法的性能，并提出了一种新型的蒙特卡洛期望 - 最大化算法（MCEM）算法，以实现一种此类模型的一种一般类型。
Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to change the underlying Gaussian distributions to multivariate $t$-distributions. Based on the representation of $t$-distribution as a scale mixture of Gaussian distributions, a hierarchical model is used for implementation. However, in the existing literature, the hierarchical model implemented does not yield the equivalent interpretation. In this paper, we present two sets of equivalent relationships between the high-level multivariate $t$-PPCA framework and the hierarchical model used for implementation. In doing so, we clarify a current misrepresentation in the literature, by specifying the correct correspondence. In addition, we discuss the performance of different multivariate $t$ robust PPCA methods both in theory and simulation studies, and propose a novel Monte Carlo expectation-maximization (MCEM) algorithm to implement one general type of such models.
