Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed. (arXiv:2203.09179v2 [math.ST] UPDATED)

Gaussian process regression underpins countless academic and industrial
applications of machine learning and statistics, with maximum likelihood
estimation routinely used to select appropriate parameters for the covariance
kernel. However, it remains an open problem to establish the circumstances in
which maximum likelihood estimation is well-posed, that is, when the
predictions of the regression model are insensitive to small perturbations of
the data. This article identifies scenarios where the maximum likelihood
estimator fails to be well-posed. These failure cases occur in …

arxiv likelihood math maximum likelihood estimation process regression