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Abstract

In many regression tasks, in addition to an accurate estimate of the conditional mean of the target distribution, an indication of the
predictive uncertainty is also required. There are two principal sources
of this uncertainty: the noise process contaminating the data and the
uncertainty in estimating the model parameters based on a limited sample
of training data. Both of them can be summarised in the predictive
variance which can then be used to give confidence intervals. In this paper,
we present various schemes for providing predictive variances for
kernel ridge regression, especially in the case of a heteroscedastic regression,
where the variance of the noise process contaminating the data is
a smooth function of the explanatory variables. The use of leave-one-out
cross-validation is shown to eliminate the bias inherent in estimates of
the predictive variance. Results obtained on all three regression tasks
comprising the predictive uncertainty challenge demonstrate the value
of this approach.