A Road to Classification in High-Dimensional Space

• Activity Number: 483
• Type: Invited
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jianqing Fan and Yang Feng*+ and Xin Tong
• Companies: Princeton University and Columbia University and Princeton University
• Keywords: ROAD ; RAID ; high dimensional classification ; Fisher Rule ; Independence Rule

Abstract

For high-dimensional classification, researchers proposed independence rules to circumvent the diverse spectra, and sparse independence rule to mitigate the issue of noise accumulation. However, in biological applications, there are often a group of correlated genes responsible for clinical outcomes, and the use of the covariance information can significantly reduce misclassification rates. The extent of such error rate reductions is unveiled by comparing the misclassification rates of the Fisher discriminant rule and the independence rule. To materialize the gain based on finite samples, a Regularized Optimal Affine Discriminant (ROAD) is proposed based on a covariance penalty. Inspired by ROAD, a Regularized Affine Independence Discriminant (RAID) is also proposed to improve independence rules. An efficient constrained coordinate-wise descent algorithm (CCD) is also developed to solve the optimization problem associated with the ROAD and RAID. Oracle type of sampling properties are established. Simulation studies and real data analysis support our theoretical results and demonstrate the advantages of the new classification procedure under a variety of correlation structures.