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# Pseudo-Bayesian Learning via Direct Loss Minimization with Applications to Sparse Gaussian Process Models

*Proceedings of The 2nd Symposium on Advances in Approximate Bayesian Inference*, PMLR 118:1-18, 2020.

#### Abstract

We propose that approximate Bayesian algorithms should optimize a new criterion, directly derived from the loss, to calculate their approximate posterior which we refer to as pseudo-posterior. Unlike standard variational inference which optimizes a lower bound on the log marginal likelihood, the new algorithms can be analyzed to provide loss guarantees on the predictions with the pseudo-posterior. Our criterion can be used to derive new sparse Gaussian process algorithms that have error guarantees applicable to various likelihoods.