Safe Feature Elimination in Sparse Supervised Learning

TL;DR

This paper introduces a non-heuristic, guaranteed feature elimination method for sparse supervised learning problems with convex loss functions and l1-penalties, significantly reducing problem size and computational effort.

Contribution

It proposes a fast, guaranteed feature elimination framework applicable to various models like SVMs, logistic regression, and least squares, enabling scalable sparse learning.

Findings

Dramatic dimensionality reduction in text classification datasets

Significant decrease in computational effort for sparse classifiers

Method extends the applicability of existing algorithms to larger datasets

Abstract

We investigate fast methods that allow to quickly eliminate variables (features) in supervised learning problems involving a convex loss function and a $l_1$-norm penalty, leading to a potentially substantial reduction in the number of variables prior to running the supervised learning algorithm. The methods are not heuristic: they only eliminate features that are {\em guaranteed} to be absent after solving the learning problem. Our framework applies to a large class of problems, including support vector machine classification, logistic regression and least-squares. The complexity of the feature elimination step is negligible compared to the typical computational effort involved in the sparse supervised learning problem: it grows linearly with the number of features times the number of examples, with much better count if data is sparse. We apply our method to data sets arising in text classification and observe a dramatic reduction of the dimensionality, hence in computational effort required to solve the learning problem, especially when very sparse classifiers are sought. Our method allows to immediately extend the scope of existing algorithms, allowing us to run them on data sets of sizes that were out of their reach before.