We present a simple algorithm for identifying and correcting real-valued
noisy labels from a mixture of clean and corrupted sample points using Gaussian
process regression. A heteroscedastic noise model is employed, in which
additive Gaussian noise terms with independent variances are associated with
each and all of the observed labels. Optimizing the noise model using maximum
likelihood estimation leads to the containment of the GPR model's predictive
error by the posterior standard deviation in leave-one-out cross-validation. A
multiplicative update scheme is proposed for solving the maximum likelihood
estimation problem under non-negative constraints. While we provide proof of
convergence for certain special cases, the multiplicative scheme has
empirically demonstrated monotonic convergence behavior in virtually all our
numerical experiments. We show that the presented method can pinpoint corrupted
sample points and lead to better regression models when trained on synthetic
and real-world scientific data sets
