= Solution
\b[<Gaussian process regression> supplies a <predictive distribution> and uncertainty estimates.] A <Gaussian process regression posterior> gives both a <posterior mean> and a <posterior variance>, allowing <credible intervals> for the latent function and a <posterior predictive distribution> for future noisy observations. The <kernel ridge regression> estimator by itself specifies a point estimate.
With the same <positive-semidefinite kernel> and matching regularization, the <Gaussian process regression> <posterior mean> equals the <kernel ridge regression> prediction. Thus the main additional benefit is the explicit <probability distribution> of predictions, conditional on the chosen <Gaussian process> model and its hyperparameters, rather than an automatic improvement in point-prediction accuracy.
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