Rui Li

Rui Li, ST John, Arno Solin

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

Rui Li, ST John, Arno Solin

Gaussian process training decomposes into inference of the (approximate) posterior and learning of the hyperparameters. For non-Gaussian (non-conjugate) likelihoods, two common choices for approximate inference are Expectation Propagation (EP) and Variational Inference (VI), which have complementary strengths and weaknesses. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, it does not automatically imply it is a good learning objective for hyperparameter optimization. We design a hybrid training procedure where the inference leverages conjugate-computation VI and the learning uses an EP-like marginal likelihood approximation. We empirically demonstrate on binary classification that this provides a good learning objective and generalizes better.