Related papers: PAGP: A physics-assisted Gaussian process framewor…

We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…

Gaussian processes (GPs) are flexible distributions over functions that enable high-level assumptions about unknown functions to be encoded in a parsimonious, flexible and general way. Although elegant, the application of GPs is limited by…

Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…

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…

A gentle introduction to Gaussian processes (GPs). The three parts of the document consider GPs for regression, classification, and dimensionality reduction.

Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention. We develop SigGPDE, a new scalable sparse variational inference framework…

Gaussian processes (GPs) are very widely used for modeling of unknown functions or surfaces in applications ranging from regression to classification to spatial processes. Although there is an increasingly vast literature on applications,…

This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region.…

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…

Solving partial differential equations (PDEs) efficiently and accurately remains a cornerstone challenge in science and engineering, especially for problems involving complex geometries and limited labeled data. We introduce a Physics- and…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the…

Model selection in Gaussian processes scales prohibitively with the size of the training dataset, both in time and memory. While many approximations exist, all incur inevitable approximation error. Recent work accounts for this error in the…

We introduce constrained Gaussian process (CGP), a Gaussian process model for random functions that allows easy placement of mathematical constrains (e.g., non-negativity, monotonicity, etc) on its sample functions. CGP comes with…

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…

Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…

We propose an effective and robust algorithm for identifying partial differential equations (PDEs) with space-time varying coefficients from a single trajectory of noisy observations. Identifying unknown differential equations from noisy…