A scaled gradient projection method for Bayesian learning in dynamical systems release_7cv2kusu3fef5hlcc6p5jzfiya

by Silvia Bonettini and Alessandro Chiuso and Marco Prato

Released as a article .

2014  

Abstract

A crucial task in system identification problems is the selection of the most appropriate model class, and is classically addressed resorting to cross-validation or using asymptotic arguments. As recently suggested in the literature, this can be addressed in a Bayesian framework, where model complexity is regulated by few hyperparameters, which can be estimated via marginal likelihood maximization. It is thus of primary importance to design effective optimization methods to solve the corresponding optimization problem. If the unknown impulse response is modeled as a Gaussian process with a suitable kernel, the maximization of the marginal likelihood leads to a challenging nonconvex optimization problem, which requires a stable and effective solution strategy. In this paper we address this problem by means of a scaled gradient projection algorithm, in which the scaling matrix and the steplength parameter play a crucial role to provide a meaning solution in a computational time comparable with second order methods. In particular, we propose both a generalization of the split gradient approach to design the scaling matrix in the presence of box constraints, and an effective implementation of the gradient and objective function. The extensive numerical experiments carried out on several test problems show that our method is very effective in providing in few tenths of a second solutions of the problems with accuracy comparable with state-of-the-art approaches. Moreover, the flexibility of the proposed strategy makes it easily adaptable to a wider range of problems arising in different areas of machine learning, signal processing and system identification.
In text/plain format

Archived Files and Locations

application/pdf  481.6 kB
file_5fmkh7dnhngeddxtvumggidcqm
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2014-06-25
Version   v1
Language   en ?
arXiv  1406.6603v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: e9a920bc-f063-47e0-84b0-9356314d172e
API URL: JSON