Regression with Input-dependent Noise: A Gaussian Process Treatment 论文

摘要

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 Background and Motivation A very natural approach to regression problems is to place a prior on the kinds of function that we expect, and then after observing the data to obtain a posterior. The prior can be obtained by placing ...