Related papers: Understanding Probabilistic Sparse Gaussian Proces…
For machine learning of interatomic potentials a scalable sparse Gaussian process regression formalism is introduced with a data-efficient on-the-fly adaptive sampling algorithm. With this approach, the computational cost is effectively…
Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…
Implicit Processes (IPs) represent a flexible framework that can be used to describe a wide variety of models, from Bayesian neural networks, neural samplers and data generators to many others. IPs also allow for approximate inference in…
Gaussian process is one of the most popular non-parametric Bayesian methodologies for modeling the regression problem. It is completely determined by its mean and covariance functions. And its linear property makes it relatively…
Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically…
A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
Sparse pseudo-point approximations for Gaussian process (GP) models provide a suite of methods that support deployment of GPs in the large data regime and enable analytic intractabilities to be sidestepped. However, the field lacks a…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…
We present a new framework for recycling independent variational approximations to Gaussian processes. The main contribution is the construction of variational ensembles given a dictionary of fitted Gaussian processes without revisiting any…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with…
Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach…
We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach…
Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…