Publications related to Transportation-based functional ANOVA and PCA for covariance operators

Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces

We study the homogenization of the Poisson equation with a reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spa ...

OXFORD UNIV PRESS2023

Testing For The Rank Of A Covariance Operator

Victor Panaretos

How can we discern whether the covariance operator of a stochastic pro-cess is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional dat ...

INST MATHEMATICAL STATISTICS-IMS2022

CovNet: Covariance networks for functional data on multidimensional domains

Victor Panaretos, Soham Sarkar

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address ...

WILEY2022

Covariance Estimation for Random Surfaces beyond Separability

Tomas Masák

This thesis focuses on non-parametric covariance estimation for random surfaces, i.e.~functional data on a two-dimensional domain. Non-parametric covariance estimation lies at the heart of functional data analysis, andconsiderations of statistical and comp ...

EPFL2022

A Characterisation Of The Continuum Gaussian Free Field In Arbitrary Dimensions

Juhan Aru

We prove that under certain mild moment and continuity assumptions, the d-dimensional continuum Gaussian free field is the only stochastic process satisfying the usual domain Markov property and a scaling assumption. Our proof is based on a decomposition o ...

ECOLE POLYTECHNIQUE2022

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

Georges Meylan, Yi Wang, Richard Massey

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. Methods. By analysing 1000 Euclid-like light cones, ...

EDP SCIENCES S A2021

Convergence of adaptive algorithms for constrained weakly convex optimization

Volkan Cevher, Ahmet Alacaoglu, Yurii Malitskyi

We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the

\tilde O(t^{-1/2})

rate of convergence for the squared norm of the gradient of Moreau envelope, ...

2021

NovelT2Mapping for Evaluating Cervical Cancer Features by Providing QuantitativeT2Maps and Synthetic Morphologic Images: A Preliminary Study

Tobias Kober, Tom Hilbert, Yong Zhang, Meng Yang, Jie Liu

Background The application value of T(2)mapping in evaluating cervical cancer (CC) features remains unclear. Purpose To investigate the role of T(2)values in evaluating CC classification, grade, and lymphovascular space invasion (LVSI) in comparison to app ...

WILEY2020

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

Strategy to validate sensor-placement methodologies in the context of sparse measurement in complex urban systems

Ian Smith, Numa Joy Bertola, Alberto Costa

The Internet of Things creates opportunities to develop data-driven design methodologies for smart cities. However, effects rather than causes are often measured in complex urban systems, requiring robust data-interpretation methodologies. Additionally, ef ...

2020

Transportation-based functional ANOVA and PCA for covariance operators

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Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces

Testing For The Rank Of A Covariance Operator

CovNet: Covariance networks for functional data on multidimensional domains

Covariance Estimation for Random Surfaces beyond Separability

A Characterisation Of The Continuum Gaussian Free Field In Arbitrary Dimensions

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

Convergence of adaptive algorithms for constrained weakly convex optimization

NovelT2Mapping for Evaluating Cervical Cancer Features by Providing QuantitativeT2Maps and Synthetic Morphologic Images: A Preliminary Study

Certified And Fast Computations With Shallow Covariance Kernels

Strategy to validate sensor-placement methodologies in the context of sparse measurement in complex urban systems

Testing For The Rank Of A Covariance Operator

CovNet: Covariance networks for functional data on multidimensional domains

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

NovelT2Mapping for Evaluating Cervical Cancer Features by Providing QuantitativeT2Maps and Synthetic Morphologic Images: A Preliminary Study

Convergence of adaptive algorithms for constrained weakly convex optimization

Strategy to validate sensor-placement methodologies in the context of sparse measurement in complex urban systems

Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces

Covariance Estimation for Random Surfaces beyond Separability

A Characterisation Of The Continuum Gaussian Free Field In Arbitrary Dimensions

Certified And Fast Computations With Shallow Covariance Kernels