Related papers: Implicit Manifold Gaussian Process Regression
This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the geometry of the data. This type of embedding first appeared…
We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…
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…
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…
This article focuses on drawing computationally-efficient predictive inference from Gaussian process (GP) regressions with a large number of features when the response is conditionally independent of the features given the projection to a…
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…
Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…
We develop Bayesian machine learning methods for mixed data sampling (MIDAS) regressions. This involves handling frequency mismatches and specifying functional relationships between many predictors and the dependent variable. We use…
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…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…
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…
Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the…
Though the underlying fields associated with vector-valued environmental data are continuous, observations themselves are discrete. For example, climate models typically output grid-based representations of wind fields or ocean currents,…
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…
This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…
Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…
Gaussian processes are notorious for scaling cubically with the size of the training set, preventing application to very large regression problems. Computation-aware Gaussian processes (CAGPs) tackle this scaling issue by exploiting…
High-dimensional data are often assumed to lie on lower-dimensional manifolds. We study how to construct diffusion processes on this data manifold using only point cloud samples and without access to charts, projections, or other geometric…