相关论文: Integrated Pre-Processing for Bayesian Nonlinear S…

Gaussian processes (GPs) are widely used in non-parametric Bayesian modeling, and play an important role in various statistical and machine learning applications. In a variety tasks of uncertainty quantification, generating random sample…

Gaussian process (GP) is a Bayesian model which provides several advantages for regression tasks in machine learning such as reliable quantitation of uncertainty and improved interpretability. Their adoption has been precluded by their…

This paper deals with the problem of adaptive output regulation for multivariable nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. The approach builds on the recently proposed adaptive internal…

We introduce graph gamma process (GGP) linear dynamical systems to model real-valued multivariate time series. For temporal pattern discovery, the latent representation under the model is used to decompose the time series into a…

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…

The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model…

Gaussian processes (GPs) are widely used as surrogate models for emulating computer code, which simulate complex physical phenomena. In many problems, additional boundary information (i.e., the behavior of the phenomena along input…

Developing suitable approximate models for analyzing and simulating complex nonlinear systems is practically important. This paper aims at exploring the skill of a rich class of nonlinear stochastic models, known as the conditional Gaussian…

Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Differential Equation (DE) is a commonly used modeling method in various scientific subjects such as finance and biology. The parameters in DE models often have interesting scientific interpretations, but their values are often unknown and…

Gaussian Process Regression (GPR) is a powerful tool for nonparametric regression, but its application in a fully Bayesian fashion in high-dimensional settings is hindered by two primary challenges: the difficulty of variable selection and…

The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…

Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…

We present a novel Kalman filter for spatiotemporal systems called the numerical Gaussian process Kalman filter (GPKF). Numerical Gaussian processes have recently been introduced as a physics informed machine learning method for simulating…

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both…

Feedforward control is essential to achieving good tracking performance in positioning systems. The aim of this paper is to develop an identification strategy for inverse models of systems with nonlinear dynamics of unknown structure using…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

Due to the increasing complexity of technical systems, accurate first principle models can often not be obtained. Supervised machine learning can mitigate this issue by inferring models from measurement data. Gaussian process regression is…

This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the…