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A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set

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Sequential Domain Adaptation by Synthesizing Distributionally Robust Experts

Daniel Kuhn, Viet Anh Nguyen, Bahar Taskesen

Least squares estimators, when trained on a few target domain samples, may predict poorly. Supervised domain adaptation aims to improve the predictive accuracy by exploiting additional labeled training samples from a source distribution that is close to th ...

2021

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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

Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

Daniel Kuhn, Viet Anh Nguyen, Peyman Mohajerin Esfahani

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a p-dimensional Gaussian random vector from n independent samples. The proposed model minimizes the worst ...

2020

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

Hybrid regularisation and the (in)admissibility of ridge regression in infinite dimensional Hilbert spaces

Victor Panaretos, Anirvan Chakraborty

We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a regularised estimation p ...

2019

Central limit theorems for multilevel Monte Carlo methods

Sebastian Krumscheid, Hakon Andreas Hoel

In this work, we show that uniform integrability is not a necessary condition for central limit theorems (CLT) to hold for normalized multilevel Monte Carlo (MLMC) estimators and we provide near optimal weaker conditions under which the CLT is achieved. In ...

2019

Adversarial Analytics

Viet Anh Nguyen

Adversarial learning is an emergent technique that provides better security to machine learning systems by deliberately protecting them against specific vulnerabilities of the learning algorithms. Many adversarial learning problems can be cast equivalently ...

EPFL2019

Statistical Applications of Random Matrix Theory: Comparison of Two Populations

Rémy Mariétan

During the last twenty years, Random matrix theory (RMT) has produced numerous results that allow a better understanding of large random matrices. These advances have enabled interesting applications in the domain of communication. Although this theory can ...

EPFL2019

Comment: Models Are Approximations!

Anthony Christopher Davison, Erwan Fabrice Koch, Jonathan Koh Boon Han

This discussion focuses on areas of disagreement with the papers, particularly the target of inference and the case for using the robust 'sandwich' variance estimator in the presence of moderate mis-specification. We also suggest that existing procedures m ...

INST MATHEMATICAL STATISTICS2019

Recovering covariance from functional fragments

Victor Panaretos, Marie-Hélène Descary

We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is observed only on a subinterval of length , one has no statistical information on ...

2019