Related papers: How Deep Are Deep Gaussian Processes?

Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…

A Neyman-Scott process is a special case of a Cox process. The latent and observable stochastic processes are both Poisson processes. We consider a deep Neyman-Scott process in this paper, for which the building components of a network are…

Complex-valued Gaussian processes are used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same model could…

Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…

Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to…

Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating…

We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…

Study of neural networks with infinite width is important for better understanding of the neural network in practical application. In this work, we derive the equivalence of the deep, infinite-width maxout network and the Gaussian process…

Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

A large collection of time series poses significant challenges for classical and neural forecasting approaches. Classical time series models fail to fit data well and to scale to large problems, but succeed at providing uncertainty…

We propose a practical and scalable Gaussian process model for large-scale nonlinear probabilistic regression. Our mixture-of-experts model is conceptually simple and hierarchically recombines computations for an overall approximation of a…

We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…

Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…

Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to…

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally…

Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…

Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…