Related papers: Explicit constructions of operator scaling Gaussia…
We propose an aggregated random-field model, and investigate the scaling limits of the aggregated partial-sum random fields. In our model, each copy of the random field in the aggregation is built from two correlated one-dimensional random…
This paper present a construction and the analysis of a class of non-Gaussian positive-definite matrix-valued homogeneous random fields with uncertain spectral measure for stochastic elliptic operators. Then the stochastic elliptic boundary…
This paper presents two new models of oriented texture, based on a new class of Gaussian fields, called locally anisotropic fractional Brownian fields, with prescribed local orientation at any point. These fields are a local version of a…
Studying the geometry generated by Gaussian and Gaussian- related random fields via their excursion sets is now a well developed and well understood subject. The purely non-Gaussian scenario has, however, not been studied at all. In this…
The Gaussian random field (GRF) and the Gaussian Markov random field (GMRF) have been widely used to accommodate spatial dependence under the generalized linear mixed model framework. These models have limitations rooted in the symmetry and…
Gaussian random fields are among the most important models of amorphous spatial structures and appear across length scales in a variety of physical, biological, and geological applications, from composite materials to geospatial data.…
In this paper a new approach for constructing \emph{multivariate} Gaussian random fields (GRFs) using systems of stochastic partial differential equations (SPDEs) has been introduced and applied to simulated data and real data. By solving a…
We review the construction of Lagrangians for higher spin fields of mixed symmetry in the framework of graded geometry. The main advantage of the graded formalism in this context is that it provides universal expressions, in the sense that…
We study the application of graph random features (GRFs) - a recently introduced stochastic estimator of graph node kernels - to scalable Gaussian processes on discrete input spaces. We prove that (under mild assumptions) Bayesian inference…
We provide a method for fast and exact simulation of Gaussian random fields on spheres having isotropic covariance functions. The method proposed is then extended to Gaussian random fields defined over spheres cross time and having…
We construct classes of homogeneous random fields on a three-dimensional Euclidean space that take values in linear spaces of tensors of a fixed rank and are isotropic with respect to a fixed orthogonal representation of the group of…
Generative Adversarial Networks (GANs) are a class of artificial neural network that can produce realistic, but artificial, images that resemble those in a training set. In typical GAN architectures these images are small, but a variant…
Reconstructing semantic-aware 3D scenes from sparse views is a challenging yet essential research direction, driven by the demands of emerging applications such as virtual reality and embodied AI. Existing per-scene optimization methods…
In this paper we will consider the problem of the numerical simulation of non-Gaussian, scalar random fields with a prescribed correlation structure provided either by a theoretical model or computed on a set of observational data.…
Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be…
Two classes of multivariate random fields with operator-stable marginals are constructed. The random fields $\mathbb{X}=\{X(t) : t \in \mathbb{R}^d \}$ with values in $\mathbb{R}^m$ are invariant in law under operator-scaling in both the…
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the…
Occupancy prediction infers fine-grained 3D geometry and semantics from camera images of the surrounding environment, making it a critical perception task for autonomous driving. Existing methods either adopt dense grids as scene…
Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…
Current statistics literature on statistical inference of random fields typically assumes that the fields are stationary or focuses on models of non-stationary Gaussian fields with parametric/semiparametric covariance families, which may…