LASSO for streaming data with adaptative filtering

Streaming data is ubiquitous in modern machine learning, and so the development of scalable algorithms to analyze this sort of information is a topic of current interest. On the other hand, the problem of l1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_1$$\end{document}-penalized least-square regression, commonly referred to as LASSO, is a quite popular data mining technique, which is commonly used for feature selection. In this work, we develop a homotopy-based solver for LASSO, on a streaming data context, that massively speeds up its convergence by extracting the most information out of the solution prior receiving the latest batch of data. Since these batches may show a non-stationary behavior, our solver also includes an adaptive filter that improves the predictability of our method in this scenario. Besides different theoretical properties, we additionally compare empirically our solver to the state-of-the-art: LARS, coordinate descent and Garrigues and Ghaoui’s data streaming homotopy. The obtained results show our approach to massively reduce the computational time require to convergence for the previous approaches, reducing up to 3, 4 and 5 orders of magnitude of running time with respect to LARS, coordinate descent and Garrigues and Ghaoui’s homotopy, respectively.