Related papers: Statistical Mechanical Analysis of Gaussian Proces…

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…

In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is…

Gaussian processes (GPs) are widely-used tools in spatial statistics and machine learning and the formulae for the mean function and covariance kernel of a GP $T u$ that is the image of another GP $u$ under a linear transformation $T$…

Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…

Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…

The use of Gaussian process models is typically limited to datasets with a few tens of thousands of observations due to their complexity and memory footprint. The two most commonly used methods to overcome this limitation are 1) the…

With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…

In Gaussian graphical models, conditional independence and partial correlations are natural inferential targets for understanding direct relationships in multivariate data. No comparable framework exists for spatial processes, where…

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…

Nonparametric Bayesian approaches based on Gaussian processes have recently become popular in the empirical learning community. They encompass many classical methods of statistics, like Radial Basis Functions or various splines, and are…

A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes,…

The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…

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…

Established techniques for simulation and prediction with Gaussian process (GP) dynamics often implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error…

Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…

We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

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…

This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…