Directed Principal Component Analysis
成果类型：
Article
署名作者：
Kao, Yi-Hao; Van Roy, Benjamin
署名单位：
Stanford University
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.2014.1290
发表日期：
2014
页码：
957-972
关键词：
摘要：
We consider a problem involving estimation of a high-dimensional covariance matrix that is the sum of a diagonal matrix and a low-rank matrix, and making a decision based on the resulting estimate. Such problems arise, for example, in portfolio management, where a common approach employs principal component analysis (PCA) to estimate factors used in constructing the low-rank term of the covariance matrix. The decision problem is typically treated separately, with the estimated covariance matrix taken to be an input to an optimization problem. We propose directed PCA, an efficient algorithm that takes the decision objective into account when estimating the covariance matrix. Directed PCA effectively adjusts factors that would be produced by PCA so that they better guide the specific decision at hand. We demonstrate through computational studies that directed PCA yields significant benefit, and we prove theoretical results establishing that the degree of improvement over conventional PCA can be arbitrarily large.