Penalized estimation in large-scale generalized linear array models

TL;DR

This paper introduces a scalable, matrix-free algorithm for penalized estimation in large-scale generalized linear array models, effectively handling high-dimensional data and nondifferentiable penalties.

Contribution

A novel design matrix free algorithm for penalized maximum likelihood estimation in GLAMs, implemented in the R package glamlasso+, which improves scalability and efficiency.

Findings

Algorithm converges reliably on large datasets

Performance surpasses glmnet in high-dimensional settings

Efficiently handles nondifferentiable penalties

Abstract

Large-scale generalized linear array models (GLAMs) can be challenging to fit. Computation and storage of its tensor product design matrix can be impossible due to time and memory constraints, and previously considered design matrix free algorithms do not scale well with the dimension of the parameter vector. A new design matrix free algorithm is proposed for computing the penalized maximum likelihood estimate for GLAMs, which, in particular, handles nondifferentiable penalty functions. The proposed algorithm is implemented and available via the R package \verb+glamlasso+. It combines several ideas -- previously considered separately -- to obtain sparse estimates while at the same time efficiently exploiting the GLAM structure. In this paper the convergence of the algorithm is treated and the performance of its implementation is investigated and compared to that of \verb+glmnet+ on simulated as well as real data. It is shown that the computation time for