Improving Hyperparameter Learning under Approximate Inference in Gaussian Process Models
This work addresses a specific bottleneck in Gaussian process modeling for researchers and practitioners, offering an incremental improvement over existing methods.
The paper tackles the problem of hyperparameter learning in Gaussian process models with non-conjugate likelihoods, showing that a hybrid training procedure combining variational inference for inference and an Expectation Propagation-like approximation for hyperparameter optimization improves performance across multiple datasets.
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.