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Structure-exploiting interior-point solver for high-dimensional entropy-sparsified regression learning

Informazioni aggiuntive

Autori
Vecchi E., Kardoš J., Lechekhab M., Waechter A., Horenko I., Schenk O.
Tipo
Articolo pubblicato in rivista scientifica
Anno
2024
Lingua
Inglese
Abstract
The solution of high-dimensional nonlinear regression problems through standard machine learning approaches often relies on first-order information, due to the numerical and memory challenges arising from the computation of the Hessian matrix and of the higher-order derivatives. While this scenario seems not favorable to second-order methods, here we show that an efficient and modular structure-exploiting interior-point solver can be successfully applied to the recently introduced class of entropy-based methods for regression learning. Specifically, by exploiting the favorable structure of the problem and of the Hessian matrix, we suggest a robust solution strategy based on explicit low-rank updates combined with an iterative Symmetric Quasi-Minimal Residual (SQMR) algorithm to solve the underlying system of linear equations. The results show that the proposed structure-exploiting solver - which relies on the hybrid parallelism and distributed-memory computing paradigm - allows a significant solution time speed-up with respect to a naive solution strategy. Furthermore, through an adequate use of the Message Passing Interface (MPI) and of Open Multi-Processing (OpenMP), the proposed solver enables the solution of large-scale problems on high-performance computing architectures consisting of thousands of compute nodes. The accompanying detailed convergence and performance analyses demonstrate both numerical robustness and high-performance capabilities for increasingly high-dimensional problems.
Rivista
Journal of Computational Science
Mese
gennaio
Pagina inizio
1
Pagina fine
30
Parole chiave
Structure-exploiting interior-point solver, Regression learning