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Activity Number: 43
Type: Contributed
Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract #314965 View Presentation
Title: The Estimation of the Noise Variance in High-Dimensional PPCA Model and Its Applications
Author(s): Zhaoyuan Li* and Jianfeng Yao and Damien Passemier
Companies: The University of Hong Kong and The University of Hong Kong and The Hong Kong University of Science and Technology
Keywords: Probabilistic principal component analysis ; high-dimensional data ; random matrix theory ; noise variance estimator ; number of principal components ; goodness-of-fit
Abstract:

We develop new statistical theory for probabilistic principal component analysis (PPCA) models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of variables is large in comparison with the sample size. We first unveil the reasons of an observed downward bias of the maximum likelihood estimator of the noise variance when the data dimension is high. We then propose a bias-corrected estimator using random matrix theory and establish its asymptotic normality. The superiority of the new estimator over existing alternatives is first checked by Monte-Carlo experiments. In order to demonstrate further potential benefits from the results of the paper to general probability PCA analysis, we provide strong evidence for net improvements in two popular procedures (Ulfarsson and Solo, 2008; Bai and Ng, 2002) for determining the number of principal components when the respective variance estimator proposed by these authors is replaced by the bias-corrected estimator. The new estimator is also used to derive new asymptotic for the related goodness-of-fit statistic under the high-dimensional scheme.


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