Zhang, Yongquan, Li, Youmei, Sun, Jianyong and Ji, Jiabing (2015) Estimates on compressed neural networks regression. Neural Networks, 63. pp. 10-17. ISSN 0893-6080 (doi:10.1016/j.neunet.2014.10.008)

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Abstract

When the neural element number nn of neural networks is larger than the sample size mm, the overfitting problem arises since there are more parameters than actual data (more variable than constraints). In order to overcome the overfitting problem, we propose to reduce the number of neural elements by using compressed projection AA which does not need to satisfy the condition of Restricted Isometric Property (RIP). By applying probability inequalities and approximation properties of the feedforward neural networks (FNNs), we prove that solving the FNNs regression learning algorithm in the compressed domain instead of the original domain reduces the sample error at the price of an increased (but controlled) approximation error, where the covering number theory is used to estimate the excess error, and an upper bound of the excess error is given.

Item Type:	Article
Additional Information:	Accepted manuscripts are Articles in Press that have been peer reviewed and accepted for publication by the Editorial Board of this publication. They have not yet been copy edited and/or formatted in the publication house style, and may not yet have the full ScienceDirect functionality, e.g., supplementary files may still need to be added, links to references may not resolve yet etc. The text could still change before final publication. Although accepted manuscripts do not have all bibliographic details available yet, they can already be cited using the year of online publication and the DOI, as follows: author(s), article title, Publication (year), DOI. When the final article is assigned to an volumes/issues of the Publication, the Article in Press version will be removed and the final version will appear in the associated published volumes/issues of the Publication. The date the article was first made available online will be carried over.
Uncontrolled Keywords:	regression learning, neural networks, compressed projection
Subjects:	B Philosophy. Psychology. Religion > BF Psychology Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General)
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science
Last Modified:	11 Nov 2016 01:38
URI:	http://gala.gre.ac.uk/id/eprint/12516

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