%0 Journal Article %1 hadji2019trust %A Hadji, Amine %A Szábo, Botond %D 2019 %K bayesian gaussian-proceses uncertainty %T Can we trust Bayesian uncertainty quantification from Gaussian process priors with squared exponential covariance kernel? %U http://arxiv.org/abs/1904.01383 %X We investigate the frequentist coverage properties of credible sets resulting in from Gaussian process priors with squared exponential covariance kernel. First we show that by selecting the scaling hyper-parameter using the maximum marginal likelihood estimator in the (slightly modified) squared exponential covariance kernel the corresponding credible sets will provide overconfident, misleading uncertainty statements for a large, representative subclass of the functional parameters in context of the Gaussian white noise model. Then we show that by either blowing up the credible sets with a logarithmic factor or modifying the maximum marginal likelihood estimator with a logarithmic term one can get reliable uncertainty statement and adaptive size of the credible sets under some additional restriction. Finally we demonstrate on a numerical study that the derived negative and positive results extend beyond the Gaussian white noise model to the nonparametric regression and classification models for small sample sizes as well.

@article{hadji2019trust, abstract = {We investigate the frequentist coverage properties of credible sets resulting in from Gaussian process priors with squared exponential covariance kernel. First we show that by selecting the scaling hyper-parameter using the maximum marginal likelihood estimator in the (slightly modified) squared exponential covariance kernel the corresponding credible sets will provide overconfident, misleading uncertainty statements for a large, representative subclass of the functional parameters in context of the Gaussian white noise model. Then we show that by either blowing up the credible sets with a logarithmic factor or modifying the maximum marginal likelihood estimator with a logarithmic term one can get reliable uncertainty statement and adaptive size of the credible sets under some additional restriction. Finally we demonstrate on a numerical study that the derived negative and positive results extend beyond the Gaussian white noise model to the nonparametric regression and classification models for small sample sizes as well.}, added-at = {2019-08-07T22:01:03.000+0200}, author = {Hadji, Amine and Szábo, Botond}, biburl = {https://www.bibsonomy.org/bibtex/205b7e5ef50716c3cba689ba9067cacea/kirk86}, description = {[1904.01383] Can we trust Bayesian uncertainty quantification from Gaussian process priors with squared exponential covariance kernel?}, interhash = {e871aca694b2f9a0099f6f8d1f0f8d81}, intrahash = {05b7e5ef50716c3cba689ba9067cacea}, keywords = {bayesian gaussian-proceses uncertainty}, note = {cite arxiv:1904.01383}, timestamp = {2019-08-07T22:01:03.000+0200}, title = {Can we trust Bayesian uncertainty quantification from Gaussian process priors with squared exponential covariance kernel?}, url = {http://arxiv.org/abs/1904.01383}, year = 2019 }