Oracle inequalities for sign constrained generalized linear models

TL;DR

This paper establishes theoretical guarantees for sign-constrained generalized linear models, demonstrating their efficiency in high-dimensional sparse regression without the need for tuning parameters, and confirms findings through numerical experiments.

Contribution

It generalizes oracle inequalities for sign-constrained models from linear to broader generalized linear models, including logistic and quantile regressions.

Findings

Sign-constrained models are as effective as oracle methods under certain conditions.

Theoretical bounds are extended to logistic and quantile regression models.

Numerical experiments support the theoretical results.

Abstract

High-dimensional data have recently been analyzed because of data collection technology evolution. Although many methods have been developed to gain sparse recovery in the past two decades, most of these methods require selection of tuning parameters. As a consequence of this feature, results obtained with these methods heavily depend on the tuning. In this paper we study the theoretical properties of sign-constrained generalized linear models with convex loss function, which is one of the sparse regression methods without tuning parameters. Recent studies on this topic have shown that, in the case of linear regression, sign-constrains alone could be as efficient as the oracle method if the design matrix enjoys a suitable assumption in addition to a traditional compatibility condition. We generalize this kind of result to a much more general model which encompasses the logistic and quantile regressions. We also perform some numerical experiments to confirm theoretical findings obtained in this paper.