Regression with input-dependent noise: A Gaussian process treatment (1998) [15 citations — 1 self]
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@INPROCEEDINGS{Goldberg98regressionwith,author = {Paul W. Goldberg and Christopher K. I. Williams and Christopher M. Bishop},
title = {Regression with input-dependent noise: A Gaussian process treatment},
booktitle = {In Advances in Neural Information Processing Systems 10},
year = {1998},
pages = {493--499},
publisher = {MIT Press}
}
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Abstract:
Gaussian processes provide natural non-parametric prior distributions over regression functions. In this paper we consider regression problems where there is noise on the output, and the variance of the noise depends on the inputs. If we assume that the noise is a smooth function of the inputs, then it is natural to model the noise variance using a second Gaussian process, in addition to the Gaussian process governing the noise-free output value. We show that prior uncertainty about the parameters controlling both processes can be handled and that the posterior distribution of the noise rate can be sampled from using Markov chain Monte Carlo methods. Our results on a synthetic data set give a posterior noise variance that well-approximates the true variance. 1
Citations
| 3172 | Neural Network for Pattern Recognition – Bishop - 1995 |
| 134 | Gaussian processes for regression – Williams, Rasmussen - 1996 |
| 94 | Evaluation of Gaussian processes and other methods for non-linear regression – Rasmussen - 1996 |
| 78 | Monte Carlo implementation of Gaussian process models for Bayesian regression and classification – Neal - 1990 |
| 44 | Mixture density networks – Bishop - 1994 |
| 26 | Prediction and Regulation by Linear Least-Squares Methods – WHITTLE - 1983 |
| 14 | Regression with input-dependent noise: a Bayesian treatment – Bishop, Qazaz - 1997 |
| 3 | Probabilistic networks: New models and new methods – MacKay - 1995 |
