We introduce Deep Sigma Point Processes, a class of parametric models inspired by the compositional structure of Deep Gaussian Processes (DGPs). Deep Sigma Point Processes (DSPPs) retain many of the attractive features of (variational) DGPs, including mini-batch training and predictive uncertainty that is controlled by kernel basis functions. Importantly, since DSPPs admit a simple maximum likelihood inference procedure, the resulting predictive distributions are not degraded by any posterior approximations. In an extensive empirical comparison on univariate and multivariate regression tasks we find that the resulting predictive distributions are significantly better calibrated than those obtained with other probabilistic methods for scalable regression, including variational DGPs--often by as much as a nat per datapoint.

The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially underestimated uncertainties. Worse still, in the regression case the predictive variance is typically dominated by observation noise, yielding uncertainty estimates that make little use of the input-dependent function uncertainty that makes GP priors attractive. In this work we propose a simple inference procedure that bypasses posterior approximations and instead directly targets the posterior predictive distribution. In an extensive empirical comparison with a number of alternative inference strategies on univariate and multivariate regression tasks, we find that the resulting predictive distributions exhibit significantly better calibrated uncertainties and higher log likelihoods--often by as much as half a nat or more per datapoint.