Approximately unbiased estimation of conditional variance in heteroscedastic kernel ridge regression

Abstract. In this paper we extend a form of kernel ridge regression for data characterised by a heteroscedastic noise process (introduced in Foxall et al. [1]) in order to provide approximately unbiased estimates of the conditional variance of the target distribution. This is achieved by the use of theleave-one-outcross-validationestimateoftheconditionalmeanwhen flttingthemodeloftheconditionalvariance. Theeliminationofthisbias isdemonstratedonsyntheticdatasetwherethetrueconditionalvariance isknown. It is well known,that the minimisation of a sum-of-squares error (SSE)