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Models of noise and robust estimates

Author: Federico Girosi; Whitaker College of Health Sciences, Technology, and Management. Center for Biological Information Processing.; Massachusetts Institute of Technology. Artificial Intelligence Laboratory.
Publisher: Cambridge, Mass. : Massachusetts Institute of Technology, Artificial Intelligence Laboratory and Center for Biological Information Processing, Whitaker College, ©1991.
Series: A.I. memo, 1287.
Edition/Format:   Book : English
Database:WorldCat
Summary:
Abstract: "Given n noisy observations g[subscript i] of the same quantity f, it is common use to give an estimate of f by minimizing the function [formula]. From a statistical point of view this corresponds to computing the Maximum Likelyhood [sic] estimate, under the assumption of Gaussian noise. However, it is well known that this choice leads to results that are very sensitive to the presence of outliers in the
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Document Type: Book
All Authors / Contributors: Federico Girosi; Whitaker College of Health Sciences, Technology, and Management. Center for Biological Information Processing.; Massachusetts Institute of Technology. Artificial Intelligence Laboratory.
OCLC Number: 27002149
Notes: Cover title.
"November 1991."
Description: 13 pages : illustrations ; 28 cm.
Series Title: A.I. memo, 1287.
Responsibility: Federico Girosi.

Abstract:

Abstract: "Given n noisy observations g[subscript i] of the same quantity f, it is common use to give an estimate of f by minimizing the function [formula]. From a statistical point of view this corresponds to computing the Maximum Likelyhood [sic] estimate, under the assumption of Gaussian noise. However, it is well known that this choice leads to results that are very sensitive to the presence of outliers in the data. For this reason it has been proposed to minimize functions of the form [formula], where V is a function that increases less rapidly than the square. Several choices for V have been proposed and successfully used to obtain 'robust' estimates.

In this paper we show that, for a class of functions V, using these robust estimators corresponds to assuming that data are corrupted by Gaussian noise whose variance fluctuates according to some given probability distribution, that uniquely determines the shape of V."

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