相关论文: Hybrid Parametric Classes of Isotropic Covariance …

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

We study the mean number counts and two-point correlation functions, along with their covariance matrices, of cosmological surveys such as for clusters. In particular, we consider correlation functions averaged over finite redshift…

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…

Geophysical and other natural processes often exhibit non-stationary covariances and this feature is important to take into account for statistical models that attempt to emulate the physical process. A convolution-based model is used to…

Functional geometry is a framework using concepts from geometry to understand the invariance of amplitudes in quantum field theory under a large class of field redefinitions, including those involving derivatives. It is inspired by…

We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory. Using Gaussian-type orbital functions, we create surrogate electronic densities of the molecule from which…

We derive a covariance formula for the class of `topological events' of smooth Gaussian fields on manifolds; these are events that depend only on the topology of the level sets of the field, for example (i) crossing events for level or…

Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…

The influence of natural image transformations on receptive field responses is crucial for modelling visual operations in computer vision and biological vision. In this regard, covariance properties with respect to geometric image…

We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval.…

Motivated by recent work involving the analysis of leveraging spatial correlations in sparsified mean estimation, we present a novel procedure for constructing covariance estimator. The proposed Random-knots (Random-knots-Spatial) and…

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…

The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…

Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…

In this note we first review the concept of D-function, closely connected with Cauchy-Schwarz inequality, and then introduce the notion of P-covariance on a Hilbert space, where $P$ is an orthogonal projection. We show that when P is…

Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…

We study covariance functions in the Gauss hypergeometric ($\mathcal{GH}$) class, a flexible family that encompasses the Generalized Wendland ($\mathcal{GW}$) and Mat\'ern ($\mathcal{MT}$) models. We derive sharp validity conditions,…

Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or…

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…