Tatjana Pavlenko: Lasso-based Estimator of the Concentration Matrix in High-Dimensional Classification

In this talk, we consider the supervised classification problem in a high-dimensional, small sample size setting. A key challenge in building an efficient classifier in such cases is estimation of the inverse covariance (concentration) matrix, and in recent years, many regularization methods were developed to cope with the high dimensionality. We suggest a two stage Lasso-based regularization procedure which allows for the block diagonal approximation of the concentration matrix. The procedure first discovers the pattern of zero in the concentration matrix corresponding to conditional independence between the feature variables and then computes the constrained maximum likelihood estimator of the covariance. We specify a class of asymptotically equivalent block structure approximations that leads to a classifier with asymptotically equal performance properties. We also propose the block-wise variable selection and investigate properties of this procedure in growing dimensions asymptotics. The relevance and benefits of the suggested approach are illustrated using both simulated and real data.