Calculation of Bayesian posteriors and model evidences typically requires numerical integration. Bayesian quadrature (BQ), a surrogate-model-based approach to numerical integration, is capable of superb sample efficiency, but its lack of parallelisation has hindered its practical applications. In this work, we propose a parallelised (batch) BQ method, employing techniques from kernel quadrature, that possesses an empirically exponential convergence rate.Additionally, just as with Nested Sampling, our method permits simultaneous inference of both posteriors and model evidence.Samples from our BQ surrogate model are re-selected to give a sparse set of samples, via a kernel recombination algorithm, requiring negligible additional time to increase the batch size.Empirically, we find that our approach significantly outperforms the sampling efficiency of both state-of-the-art BQ techniques and Nested Sampling in various real-world datasets, including lithium-ion battery analytics.

Q and P represent the number of gradient descent iterations and the number of MCMC samplings, respectively. For the other symbols, see the main text.

Gaussian Cox processes are widely-used point process models that use a Gaussian process to describe the Bayesian a priori uncertainty present in latent intensity functions. In this paper, we propose a novel Bayesian inference scheme for Gaussian Cox processes by exploiting a conceptually-intuitive { it path integral} formulation. The proposed scheme does not rely on domain discretization, scales linearly with the number of observed events, has a lower complexity than the state-of-the-art variational Bayesian schemes with respect to the number of inducing points, and is applicable to a wide range of Gaussian Cox processes with various types of link functions. Our scheme is especially beneficial under the multi-dimensional input setting, where the number of inducing points tends to be large. We evaluate our scheme on synthetic and real-world data, and show that it achieves comparable predictive accuracy while being tens of times faster than reference methods.

Calculation of Bayesian posteriors and model evidences typically requires numerical integration. Bayesian quadrature (BQ), a surrogate-model-based approach to numerical integration, is capable of superb sample efficiency, but its lack of parallelisation has hindered its practical applications. In this work, we propose a parallelised (batch) BQ method, employing techniques from kernel quadrature, that possesses an empirically exponential convergence rate.Additionally, just as with Nested Sampling, our method permits simultaneous inference of both posteriors and model evidence.Samples from our BQ surrogate model are re-selected to give a sparse set of samples, via a kernel recombination algorithm, requiring negligible additional time to increase the batch size.Empirically, we find that our approach significantly outperforms the sampling efficiency of both state-of-the-art BQ techniques and Nested Sampling in various real-world datasets, including lithium-ion battery analytics.

We present a new variational inference algorithm for Gaussian processes with non-conjugate likelihood functions. This includes binary and multi-class classification, as well as ordinal regression. Our method constructs a convex lower bound, which can be optimized by using an efficient fixed point update method. We then show empirically that our new approach is much faster than existing methods without any degradation in performance.

We present a new variational inference algorithm for Gaussian processes with non-conjugate likelihood functions. This includes binary and multi-class classification, as well as ordinal regression. Our method constructs a convex lower bound, which can be optimized by using an efficient fixed point update method. We then show empirically that our new approach is much faster than existing methods without any degradation in performance. Papers published at the Neural Information Processing Systems Conference.