2010/11/28 by Jianqing Fan, Yang Feng, Fan, Jianqing +3
Biochemistry, Genetics and Molecular Biology · Chemistry · Computer Science · #FOS: Computer and information sciences #Face and Expression Recognition #Gene expression and cancer classification #Machine Learning (stat.ML) #Methodology (stat.ME) #Spectroscopy and Chemometric Analyses
paper · pdf · doi:10.48550/arxiv.1011.6095
openalex publication_date 2010/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to circumvent the diverse spectra, and sparse independence rules 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. ROAD selects an increasing number of features as the penalization relaxes. Further benefits can be achieved when a screening method is employed to narrow the feature pool before hitting the ROAD. An efficient Constrained Coordinate Descent algorithm (CCD) is also developed to solve the associated optimization problems. Sampling properties of oracle type 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. A delicate result on continuous piecewise linear solution path for the ROAD optimization problem at the population level justifies the linear interpolation of the CCD algorithm.