Bayesian regularization and pruning using a Laplace prior
Neural Computation
Regression with input-dependent noise: a Gaussian process treatment
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Ridge Regression Learning Algorithm in Dual Variables
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Bayesian Inference of Noise Levels in Regression
ICANN 96 Proceedings of the 1996 International Conference on Artificial Neural Networks
A Generalized Representer Theorem
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
Using neural networks to model conditional multivariate densities
Neural Computation
Most likely heteroscedastic Gaussian process regression
Proceedings of the 24th international conference on Machine learning
Mining for the most certain predictions from dyadic data
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
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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.