2016/03/04 by Tomoyuki Obuchi, Obuchi, Tomoyuki, Yoshiyuki Kabashima +1
Engineering · Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Methodology (stat.ME) #Scientific Research and Discoveries #Statistical Mechanics (cond-mat.stat-mech) #Statistical and numerical algorithms #Structural Health Monitoring Techniques
paper · pdf · doi:10.48550/arxiv.1603.01399
openalex publication_date 2016/03/04 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28
The approximation of a high-dimensional vector by a small combination of\ncolumn vectors selected from a fixed matrix has been actively debated in\nseveral different disciplines. In this paper, a sampling approach based on the\nMonte Carlo method is presented as an efficient solver for such problems.\nEspecially, the use of simulated annealing (SA), a metaheuristic optimization\nalgorithm, for determining degrees of freedom (the number of used columns) by\ncross validation is focused on and tested. Test on a synthetic model indicates\nthat our SA-based approach can find a nearly optimal solution for the\napproximation problem and, when combined with the CV framework, it can optimize\nthe generalization ability. Its utility is also confirmed by application to a\nreal-world supernova data set.\n