Probabilistic Iterative Hard Thresholding for Sparse Learning

TL;DR

This paper introduces a probabilistic iterative hard thresholding method for sparse learning, providing convergence guarantees and demonstrating effectiveness on machine learning tasks in high-dimensional, noisy data environments.

Contribution

It proposes a novel probabilistic approach to iterative hard thresholding with proven convergence for sparse optimization in noisy, high-dimensional settings.

Findings

Proven convergence of the stochastic process.

Effective performance on two machine learning problems.

Addresses sparse learning in big data contexts.

Abstract

For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called "l0 norm" which counts the number of non-zero components in a vector, is a strong reliable mechanism of enforcing sparsity when incorporated into an optimization problem for minimizing the fit of a given model to a set of observations. However, in big data settings wherein noisy estimates of the gradient must be evaluated out of computational necessity, the literature is scant on methods that reliably converge. In this paper we present an approach towards solving expectation objective optimization problems with cardinality constraints. We prove convergence of the underlying stochastic process, and demonstrate the performance on two Machine Learning problems.