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Concept

Covariance function

Related publications (18)

Transportation-based functional ANOVA and PCA for covariance operators

Victor Panaretos, Yoav Zemel, Valentina Masarotto

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Inst Mathematical Statistics-Ims2024

Multivariate geometric anisotropic Cox processes

Sofia Charlotta Olhede

This paper introduces a new modeling and inference framework for multivariate and anisotropic point processes. Building on recent innovations in multivariate spatial statistics, we propose a new family of multivariate anisotropic random fields, and from th ...

WILEY2023

The Completion Of Covariance Kernels

Victor Panaretos, Kartik Waghmare

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Omega of a rectangular domain I x I to a covariance kernel on the entire domain I x I. For a broad class of domains Omega call ...

INST MATHEMATICAL STATISTICS-IMS2022

Euclid : Effects of sample covariance on the number counts of galaxy clusters

Yi Wang, Georges Meylan

Aims. We investigate the contribution of shot-noise and sample variance to uncertainties in the cosmological parameter constraints inferred from cluster number counts, in the context of the Euclid survey. ...

EDP SCIENCES S A2021

Sparsely Observed Functional Time Series: Theory and Applications

Tomas Rubin

Functional time series is a temporally ordered sequence of not necessarily independent random curves. While the statistical analysis of such data has been traditionally carried out under the assumption of completely observed functional data, it may well ha ...

EPFL2021

Certified And Fast Computations With Shallow Covariance Kernels

Daniel Kressner, Stefano Massei

Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random fields have gained ...

AMER INST MATHEMATICAL SCIENCES-AIMS2020

High-Frequency Analysis Of Parabolic Stochastic Pdes

Carsten Hao Ye Chong

We consider the problem of estimating stochastic volatility for a class of second-order parabolic stochastic PDEs. Assuming that the solution is observed at high temporal frequency, we use limit theorems for multipower variations and related functionals to ...

INST MATHEMATICAL STATISTICS2020

A Covariance Formula For Topological Events Of Smooth Gaussian Fields

Alejandro Rivera

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 excursion sets, (ii ...

INST MATHEMATICAL STATISTICS2020

Spatial covariance improves BCI performance for late ERPs components with high temporal variability

José del Rocio Millán Ruiz, Ricardo Andres Chavarriaga Lozano, Lucian Andrei Gheorghe, Marija Uscumlic, Ruslan Aydarkhanov

Objective. Event Related Potentials (ERPs) reflecting cognitive response to external stimuli, are widely used in brain computer interfaces. ERP waveforms are characterized by a series of components of particular latency and amplitude. The classical ERP dec ...

2020

Decompositions Of Log-Correlated Fields With Applications

Janne Matias Junnila

In this article, we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorems. Th ...

2019

Pairwise Comparisons with Flexible Time-Dynamics

Matthias Grossglauser, Lucas Maystre, Victor Kristof

Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We achieve this by replac ...

ASSOC COMPUTING MACHINERY2019

Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes

Victor Panaretos, Yoav Zemel, Valentina Masarotto

Covariance operators are fundamental in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loeve expansion. These operators may themselves be subject to variation, for instance in contexts wh ...

2019

SLANG: Fast Structured Covariance Approximations for Bayesian Deep Learning with Natural Gradient

Mohammad Emtiyaz Khan

Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a diagonal approxi ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Towards tailoring non-invasive brain stimulation using real-time fMRI and Bayesian optimization

Yury Koush

Non-invasive brain stimulation, such as transcranial alternating current stimulation (tACS) provides a powerful tool to directly modulate brain oscillations that mediate complex cognitive processes. While the body of evidence about the effect of tACS on be ...

Ieee2016

A Multi Level Monte Carlo Method with Control Variate for elliptic PDEs with log-normal coefficients

Fabio Nobile, Francesco Tesei

We consider the numerical approximation of the stochastic Darcy problem with log-normal permeability field and propose a novel Multi Level Monte Carlo (MLMC) approach with a control variate variance reduction technique on each level. We model the log-perme ...

2015

Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting

Andreas Krause, Matthias Seeger

Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multiarmed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low norm in a reproducing ...

Institute of Electrical and Electronics Engineers2012

Geostatistics of extremes

Anthony Christopher Davison, Mehdi Gholam

We describe a prototype approach to flexible modelling for maxima observed at sites in a spatial domain, based on fitting of max-stable processes derived from underlying Gaussian random fields. The models we propose have generalised extreme-value marginal ...

2012

Non-Ideal Sampling and Adapted Reconstruction Using the Stochastic Matérn Model

Michaël Unser, Dimitri Nestor Alice Van De Ville, Sathish Ramani

The Matérn class is a parametric family of autocorrelation functions that is commonly used in geostatistics. We argue that a generalized, anisotropic version of this model is suitable for capturing the correlation structure of a variety of natural images. ...

IEEE2006