Sparsity and Structure in Large Scale Learning and Optimization
In this talk, I introduce our recent results on the complexity of convex optimization methods for solving high-dimensional machine learning and statistical estimation problems. The primary focus of this research is hidden problem sparsity and structure that numerical algorithms could utilize to accelerate numerical algorithms of large-scale problems such as LASSO and PageRank. Further, we investigate the sparsity of classification problems and its influence on the complexity and reliability of binary and multi-class classification methods. Finally, I present some motivating engineering applications along with the results of numerical experiments justifying the efficiency of the proposed algorithms and compare them with state-of-the-art algorithms and commercial solvers.