Related papers: Gaussian Process Quantile Regression using Expecta…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
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…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…
Distributional regression aims to estimate the full conditional distribution of a target variable, given covariates. Popular methods include linear and tree-ensemble based quantile regression. We propose a neural network-based…
Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the…
Gaussian processes are probabilistic models that are commonly used as functional priors in machine learning. Due to their probabilistic nature, they can be used to capture the prior information on the statistics of noise, smoothness of the…
We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the…
Regression classes modeling more than the mean of the response have found a lot of attention in the last years. Expectile regression is a special and computationally convenient case of this family of models. Expectiles offer a quantile-like…
We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent…
This paper is concerned with the problem of how to speed up computation for Gaussian process models trained on autocorrelated data. The Gaussian process model is a powerful tool commonly used in nonlinear regression applications. Standard…
Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine…
We propose a new method for simplification of Gaussian process (GP) models by projecting the information contained in the full encompassing model and selecting a reduced number of variables based on their predictive relevance. Our results…
Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…
Regression is typically treated as a curve-fitting process where the goal is to fit a prediction function to data. With the help of conditional generative adversarial networks, we propose to solve this age-old problem in a different way; we…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
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 (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…
In this manuscript, we study the problem of scalar-on-distribution regression; that is, instances where subject-specific distributions or densities, or in practice, repeated measures from those distributions, are the covariates related to a…