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Matrix Inversion free variational inference in Conditional Student's T Processes

We propose a new variational lower bound for performing inference in sparse Student's T Processes that does not require computationally intensive operations such as matrix inversions or log determinants of matrices. We devise a mathematically valid and easy-to-sample from approximate posterior over the Inverse Wishart distributed covariance matrix encompassing both training data and inducing points. To deal with remaining log determinant terms we propose a conjugate gradient based lower bound that is tight when approximate posteriors are optimal. We demonstrate that our proposed model behaves similarly to matrix inversion dependent counterparts in terms of convergence of evidence lower bound and predictive capabilities at testing time on a wide array of toy experiments. Moreover, we test the validity of our method on medium and large scale datasets, showing encouraging results.

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