Sparse Quadratic Classification Rules via Linear Dimension Reduction

• Activity Number: 506 - Advances in Multivariate Analysis for High-Dimensional, Complex Data Problems
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Korean International Statistical Society
• Author(s): Tianying Wang* and Irina Gaynanova
• Companies: Texas A & M University and Texas A&M Univeristy
• Keywords: convex optimization; discriminant analysis; high-dimensional statistics; variable selection

Abstract

We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on original data, with the subsequent application of quadratic discriminant analysis on the reduced space. In contrast to quadratic discriminant analysis, the proposed framework doesn't require estimation of precision matrices and scales linearly with the number of measurements, making it especially attractive for the use on high-dimensional datasets. We support the methodology with theoretical guarantees on variable selection consistency, and empirical comparison with competing approaches. We apply the method to gene expression data of breast cancer patients, and confirm the crucial importance of ESR1 gene in differentiating estrogen receptor status.