A0258
Title: Constrained approaches in learning high-dimensional sparse structures: Statistical optimality and optimization tools
Authors: Shihao Wu - University of Michigan, Ann Arbor (United States) [presenting]
Abstract: Sparse structures are ubiquitous in high-dimensional statistical models. To learn sparse structures from data, penalized approaches have been widely used and studied in the past two decades. Constrained approaches, however, were understudied due to their computational intractability and have recently been regaining attention given algorithmic advances in the optimization community and hardware improvements. Constrained approaches with penalized approaches in feature selection in high-dimensional sparse linear regression are compared. Specifically, it is focused on false discovery in the early stage of the solution path, which tracks how features enter and leave the model for a selection approach. As a penalized approach, LASSO is known to suffer false discoveries in the early stage. It is shown that best subset selection (BSS), as a constrained approach, achieves exact zero false discovery throughout the early stage under an optimal condition that it is found. It is referred to as zero false discovery as sure early selection. A solution to BSS within a tolerable optimization error suffices shown to achieve sure early selection. Extensive numerical experiments also demonstrate the advantages of constrained approaches on the solution path over penalized methods. Results for high-dimensional supervised fusion and high-dimensional mediation analysis and their corresponding constrained approaches will also be introduced and discussed.
