Related papers: Evolution of Covariance Functions for Gaussian Pro…
Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…
This work proposes an extension to Structured Grammatical Evolution (SGE) called Co-evolutionary Probabilistic Structured Grammatical Evolution (Co-PSGE). In Co-PSGE each individual in the population is composed by a grammar and a genotype,…
Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…
The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…
A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…
Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
Grammar-Guided Genetic Programming (GGGP) employs a variety of insights from evolutionary theory to autonomously design solutions for a given task. Recent insights from evolutionary biology can lead to further improvements in GGGP…
We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty in covariance function…
Multivariate compositional count data arise in many applications including ecology, microbiology, genetics, and paleoclimate. A frequent question in the analysis of multivariate compositional count data is what values of a covariate(s) give…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
The construction of valid and flexible cross-covariance functions is a fundamental task for modeling multivariate space-time data arising from climatological and oceanographical phenomena. Indeed, a suitable specification of the covariance…
Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the…
The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…
Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…
Implementing Bayesian variable selection for linear Gaussian regression models for analysing high dimensional data sets is of current interest in many fields. In order to make such analysis operational, we propose a new sampling algorithm…
Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
Stochastic Process Model has many applications in analysis of longitudinal biodemographic data. Such data contain various physiological variables (sometimes known as covariates). It also can potentially contain genetic information available…