Related papers: Skew-Gaussian Random Fields
We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single-layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
Traditional MCMC algorithms are computationally intensive and do not scale well to large data. In particular, the Metropolis-Hastings (MH) algorithm requires passing over the entire dataset to evaluate the likelihood ratio in each…
Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…
The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement.…
Structure formation in our Universe creates non-Gaussian random fields that will soon be observed over almost the entire sky by the Euclid satellite, the Vera-Rubin observatory, and the Square Kilometre Array. An unsolved problem is how to…
Gaussian distributions are widely used in Bayesian variational inference to approximate intractable posterior densities, but the ability to accommodate skewness can improve approximation accuracy significantly, when data or prior…
The recently proposed non-Gaussian Mat\'{e}rn random field models, generated through Stochastic Partial differential equations (SPDEs), are extended by considering the class of Generalized Hyperbolic processes as noise forcings. The models…
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial…
We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…
We compute the skewness of the matter distribution arising from non-linear evolution and from non-Gaussian initial perturbations. We apply our result to a very generic class of models with non-Gaussian initial conditions and we estimate…
While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in…
Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a…
This paper studies a risk minimization problem with decision dependent data distribution. The problem pertains to the performative prediction setting in which a trained model can affect the outcome estimated by the model. Such dependency…
A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…
Metropolis Hastings nested sampling evolves a Markov chain, accepting new points along the chain according to a version of the Metropolis Hastings acceptance ratio, which has been modified to satisfy the nested sampling likelihood…
We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale…
We introduce local expectation gradients which is a general purpose stochastic variational inference algorithm for constructing stochastic gradients through sampling from the variational distribution. This algorithm divides the problem of…
In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…
We aim at analyzing geostatistical and areal data observed over irregularly shaped spatial domains and having a distribution within the exponential family. We propose a generalized additive model that allows to account for spatially-varying…