Regression with Input-Dependent Noise: A Bayesian Treatment

Part of Advances in Neural Information Processing Systems 9 (NIPS 1996)

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Christopher Bishop, Cazhaow Quazaz


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 hav(cid:173) ing 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 over(cid:173) coming the bias of maximum likelihood.