Penalized estimation in large-scale generalized linear array models
This work addresses computational bottlenecks for researchers and practitioners in statistics and machine learning dealing with high-dimensional tensor data, representing an incremental improvement by combining existing ideas into a scalable solution.
The paper tackles the challenge of fitting large-scale generalized linear array models (GLAMs) by proposing a new design matrix-free algorithm for penalized maximum likelihood estimation, which efficiently handles nondifferentiable penalties and exploits GLAM structure to achieve sparse estimates, as demonstrated through comparisons with glmnet on simulated and real data.
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