Sparsified-Learning for Heavy-Tailed Locally Stationary Processes

Sparsified Learning is ubiquitous in many machine learning tasks. It aims to regularize the objective function by adding a penalization term that considers the constraints made on the learned parameters. This paper considers the problem of learning heavy-tailed LSP. We develop a flexible and robust sparse learning framework capable of handling heavy-tailed data with locally stationary behavior and propose concentration inequalities. We further provide non-asymptotic oracle inequalities for different types of sparsity, including $\ell_1$-norm and total variation penalization for the least square loss.