Sparse Gaussian Processes: Structured Approximations and Power-EP Revisited
This provides incremental improvements to sparse Gaussian process methods for practitioners in machine learning who need scalable probabilistic models.
The paper tackles the problem of scaling Gaussian process models by improving sparse variational approximations, showing that block-diagonal structured approximations consistently perform similarly to or better than existing diagonal methods while maintaining comparable computational costs.
Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to the conditional posterior density given the inducing points. This paper first considers an extension that employs a block-diagonal structure for the scaling matrix, provably tightening the variational lower bound. We then revisit the unifying framework of sparse GPs based on Power Expectation Propagation (PEP) and show that it can leverage and benefit from the new structured approximate posteriors. Through extensive regression experiments, we show that the proposed block-diagonal approximation consistently performs similarly to or better than existing diagonal approximations while maintaining comparable computational costs. Furthermore, the new PEP framework with structured posteriors provides competitive performance across various power hyperparameter settings, offering practitioners flexible alternatives to standard variational approaches.