DMS Statistics and Data Science Seminar

Speaker: Xin Bing (University of Toronto)

Title: Optimal Discriminant Analysis in High-Dimensional Latent Factor Models

Abstract: In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower-dimensional space, and base the classification on the resulting lower-dimensional projections. In this paper, we formulate a latent-variable model with a hidden low-dimensional structure to justify this two-step procedure and to guide which projection to choose. We propose a computationally efficient classifier that takes certain principal components (PCs) of the observed features as projections, with the number of retained PCs selected in a data-driven way. A general theory is established for analyzing such two-step classifiers based on any projections. We derive explicit rates of convergence of the excess risk of the proposed PC-based classifier. The obtained rates are further shown to be optimal up to logarithmic factors in the minimax sense. Our theory allows the lower dimension to grow with the sample size and is also valid even when the feature dimension (greatly) exceeds the sample size. Extensive simulations corroborate our theoretical findings. The proposed method also performs favorably relative to other existing discriminant methods on three real data examples.

Short Bio. Dr. Bing holds a Ph.D. degree in statistics from Cornell University. His research interest generally lies in developing new methodologies with theoretical guarantees to tackle modern statistical problems such as high-dimensional statistics, low-rank matrix estimation, multivariate analysis, model-based clustering, latent factor model, topic models, minimax estimation, high-dimensional inference, and statistical and computational trade-offs. He is also interested in the applications of statistical methods to genetics, neuroscience, immunology, and other areas.