Probabilistic Iterative Hard Thresholding for Sparse Learning
This work addresses the problem of sparse learning for researchers and practitioners in machine learning dealing with high-dimensional data, though it appears incremental as it builds on existing iterative hard thresholding methods.
The paper tackles the challenge of reliably converging to sparse solutions in high-dimensional, noisy big data settings by introducing a probabilistic iterative hard thresholding method for expectation objective optimization with cardinality constraints, and demonstrates its performance on two machine learning problems.
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.