A Novel Framework for Online Supervised Learning with Feature Selection

TL;DR

This paper introduces a new online learning framework based on running averages that effectively incorporates regularized feature selection methods, achieving high support recovery accuracy and faster convergence than traditional approaches.

Contribution

The paper develops an online framework that extends offline regularized methods like Lasso and Elastic Net, with proven equivalence, support recovery guarantees, and improved convergence.

Findings

High true support recovery accuracy achieved

Faster convergence rates demonstrated

Competitive performance on large datasets

Abstract

Current online learning methods suffer issues such as lower convergence rates and limited capability to select important features compared to their offline counterparts. In this paper, a novel framework for online learning based on running averages is proposed. Many popular offline regularized methods such as Lasso, Elastic Net, Minimax Concave Penalty (MCP), and Feature Selection with Annealing (FSA) have their online versions introduced in this framework. The equivalence between the proposed online methods and their offline counterparts is proved, and then novel theoretical true support recovery and convergence guarantees are provided for some of the methods in this framework. Numerical experiments indicate that the proposed methods enjoy high true support recovery accuracy and a faster convergence rate compared with conventional online and offline algorithms. Finally, applications to large datasets are presented, where again the proposed framework shows competitive results compared to popular online and offline algorithms.