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This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuously specified Gaussian random field. We show that for…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…
This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
In this paper, we introduce a novel theoretical framework for Gaussian process regression error analysis, leveraging a function-space decomposition. Based on this framework, we develop a weighted Jacobi iterative method that utilizes…
Variational methods are attractive for computing Bayesian inference for highly parametrized models and large datasets where exact inference is impractical. They approximate a target distribution - either the posterior or an augmented…
Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior.…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…
Monitoring daily weather fields is critical for climate science, agriculture, and environmental planning, yet fully probabilistic spatio-temporal models become computationally prohibitive at continental scale. We present a case study on…
This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators'…
The structure of the gaussian auxiliary field approximation in the theory of phase ordering kinetics is analysed with the aim of placing the method within the context of a systematic theory. While we are unable to do this for systems with a…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient-enhanced covariance matrix can be beneficial since it provides a more…
The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…
This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…
A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…
Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such…