NDLI: Comparison of loss functions for linear regression

Content Provider	IEEE Xplore Digital Library
Author	Cherkassky, V. Yunqian Ma
Copyright Year	2004
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Minnesota Univ., Minniapolis, MN, USA (Cherkassky, V.; Yunqian Ma)
Abstract	This paper addresses selection of the loss function for regression problems with finite data. It is well-known (under standard regression formulation) that for a known noise density there exist an optimal loss function under an asymptotic setting (large number of samples), i.e. squared loss is optimal for Gaussian noise density. However, in real-life applications the noise density is unknown and the number of training samples is finite. For such practical situations, we suggest using Vapnik's /spl epsiv/-insensitive loss function. We use practical method for setting the value of /spl epsiv/ as a function of known number of samples and (known or estimated) noise variance (V. Cherkassky and Y. Ma, (2004), (2002)). We consider commonly used noise densities (such as Gaussian, Uniform and Laplacian noise). Empirical comparisons for several representative linear regression problems indicate that Vapnik's /spl epsiv/-insensitive loss yields more robust performance and improved prediction accuracy, in comparison with squared loss and least-modulus loss, especially for noisy high-dimensional data sets.
Starting Page	395
Ending Page	400
File Size	383807
Page Count	6
File Format	PDF
ISBN	0780383591
ISSN	10987576
DOI	10.1109/IJCNN.2004.1379938
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-07-25
Publisher Place	Hungary
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Linear regression Noise robustness Gaussian noise Statistics Accuracy Additive noise Parameter estimation Support vector machines Laplace equations Performance loss
Content Type	Text
Resource Type	Article

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