Related papers: Fast Approximate Multi-output Gaussian Processes

Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…

Multi-output regression problems are commonly encountered in science and engineering. In particular, multi-output Gaussian processes have been emerged as a promising tool for modeling these complex systems since they can exploit the…

Solving nonlinear partial differential equations (PDEs) using kernel methods offers a compelling alternative to traditional numerical solvers. However, the performance of these methods strongly depends on the choice of kernel. In this work,…

This paper examines experimental design procedures used to develop surrogates of computational models, exploring the interplay between experimental designs and approximation algorithms. We focus on two widely used approximation approaches,…

We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…

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…

To determine the optimal set of hyperparameters of a Gaussian process based on a large number of training data, both a linear system and a trace estimation problem must be solved. In this paper, we focus on establishing numerical methods…

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…

Deep neural networks (DNN) and Gaussian processes (GP) are two powerful models with several theoretical connections relating them, but the relationship between their training methods is not well understood. In this paper, we show that…

Gaussian Processes (GPs) provide a general and analytically tractable way of modeling complex time-varying, nonparametric functions. The Automatic Bayesian Covariance Discovery (ABCD) system constructs natural-language description of…

This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…

We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…

Gaussian processes (GPs) are flexible models that can capture complex structure in large-scale dataset due to their non-parametric nature. However, the usage of GPs in real-world application is limited due to their high computational cost…

Gaussian Mixture Models (GMMs) range among the most frequently used models in machine learning. However, training large, general GMMs becomes computationally prohibitive for datasets that have many data points $N$ of high-dimensionality…

Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…

Gaussian processes (GPs) are crucial in machine learning for quantifying uncertainty in predictions. However, their associated covariance matrices, defined by kernel functions, are typically dense and large-scale, posing significant…

Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…

Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are…

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

Gaussian processes (GPs) provide a framework for Bayesian inference that can offer principled uncertainty estimates for a large range of problems. For example, if we consider regression problems with Gaussian likelihoods, a GP model enjoys…