Regression with input-dependent noise: A Bayesian treatment

Abstract

In most treatments of the regression problem it is assumed that the distribution of target data can be described by a deterministic function of the inputs, together with additive Gaussian noise having constant variance. The use of maximum likelihood to train such models then corresponds to the minimization of a sum-of-squares error function. In many applications a more realistic model would allow the noise variance itself to depend on the input variables. However, the use of maximum likelihood to train such models would give highly biased results. In this paper we show how a Bayesian treatment can allow for an input-dependent variance while overcoming the bias of maximum likelihood.

Divisions: Aston University (General)
Additional Information: Copyright of the Massachusetts Institute of Technology Press (MIT Press)
Event Title: Advances in Neural Information Processing Systems 1994
Event Type: Other
Event Dates: 1994-11-16 - 1994-11-18
Uncontrolled Keywords: regression problem,target data,Gaussian noise,error function,noise variance
ISBN: 0262100657
Full Text Link:
Related URLs: http://mitpress ... type=2&tid=3990 (Publisher URL)
PURE Output Type: Chapter
Published Date: 1997-05
Authors: Bishop, Christopher M.
Qazaz, Cazhaow S.

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