A First-Order Optimization Algorithm for Statistical Learning with Hierarchical Sparsity Structure

In many statistical learning problems, it is desired that the optimal solution conform to an a priori known sparsity structure represented by directed acyclic graph. Inducing such structures means of convex regularizers requires nonsmooth penalty functions exploit group overlapping. Our study focuses on evaluating proximal operator latent overlapping lasso developed Jacob et al. in 2009. We implemented alternating direction method multiplier with sharing scheme solve large-scale instances underlying optimization problem efficiently. absence strong convexity, global linear convergence algorithm established using error bound theory. More specifically, paper contributes establishing primal and dual bounds when component objective function does not have polyhedral epigraph. also investigate effect graph speed algorithm. Detailed numerical simulation studies over different supporting proposed two applications are provided. Summary Contribution: The proposes computationally efficient evaluate hierarchical sparsity-inducing regularizer establishes its properties. intensive subproblem can be fully parallelized, which allows solving problem. Comprehensive benchmarking against five other methods optimality Furthermore, performance demonstrated related topic modeling breast cancer classification. code along benchmarks available corresponding author’s GitHub website for evaluation future use.