Adaptive regularization for Lasso models in the context of non-stationary data streams

TL;DR

This paper introduces an adaptive regularization framework for Lasso models in streaming data, enabling dynamic regularization parameter tuning to handle non-stationarity effectively.

Contribution

It proposes a novel online method to adaptively update the Lasso regularization parameter using stochastic gradient descent, applicable to linear and generalized linear models.

Findings

Effective in non-stationary streaming environments

Demonstrated on simulated and real datasets

Improves model sparsity and predictive stability

Abstract

Large scale, streaming datasets are ubiquitous in modern machine learning. Streaming algorithms must be scalable, amenable to incremental training and robust to the presence of non-stationarity. In this work consider the problem of learning $\ell_1$ regularized linear models in the context of streaming data. In particular, the focus of this work revolves around how to select the regularization parameter when data arrives sequentially and the underlying distribution is non-stationary (implying the choice of optimal regularization parameter is itself time-varying). We propose a framework through which to infer an adaptive regularization parameter. Our approach employs an $\ell_1$ penalty constraint where the corresponding sparsity parameter is iteratively updated via stochastic gradient descent. This serves to reformulate the choice of regularization parameter in a principled framework for online learning. The proposed method is derived for linear regression and subsequently extended to generalized linear models. We validate our approach using simulated and real datasets and present an application to a neuroimaging dataset.