Max Sommerfeld
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View article: Empirical optimal transport on countable metric spaces: Distributional limits and statistical applications
Empirical optimal transport on countable metric spaces: Distributional limits and statistical applications Open
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
View article: Optimal Transport: Fast Probabilistic Approximation with Exact Solvers
Optimal Transport: Fast Probabilistic Approximation with Exact Solvers Open
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including …
View article: Confidence Regions for Spatial Excursion Sets From Repeated Random Field Observations, With an Application to Climate
Confidence Regions for Spatial Excursion Sets From Repeated Random Field Observations, With an Application to Climate Open
The goal of this article is to give confidence regions for the excursion set of a spatial function above a given threshold from repeated noisy observations on a fine grid of fixed locations. Given an asymptotically Gaussian estimator of th…
View article: Confidence Regions for Spatial Excursion Sets From Repeated Random Field Observations, With an Application to Climate
Confidence Regions for Spatial Excursion Sets From Repeated Random Field Observations, With an Application to Climate Open
The goal of this article is to give confidence regions for the excursion set of a spatial function above a given threshold from repeated noisy observations on a fine grid of fixed locations. Given an asymptotically Gaussian estimator of th…
View article: Inference for Empirical Wasserstein Distances on Finite Spaces
Inference for Empirical Wasserstein Distances on Finite Spaces Open
Summary The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we …
View article: Confidence regions for spatial excursion sets from repeated random field observations, with an application to climate
Confidence regions for spatial excursion sets from repeated random field observations, with an application to climate Open
The goal of this paper is to give confidence regions for the excursion set of a spatial function above a given threshold from repeated noisy observations on a fine grid of fixed locations. Given an asymptotically Gaussian estimator of the …
View article: Wasserstein Distance on Finite Spaces: Statistical Inference and Algorithms
Wasserstein Distance on Finite Spaces: Statistical Inference and Algorithms Open
Wasserstein distances or, more generally, distances that quantify the optimal transport between probability measures on metric spaces have long been established as an important tool in probability theory. More recently, it has found its wa…
View article: Inference for Empirical Wasserstein Distances on Finite Spaces
Inference for Empirical Wasserstein Distances on Finite Spaces Open
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive t…
View article: Confidence regions for excursion sets in asymptotically Gaussian random fields, with an application to climate
Confidence regions for excursion sets in asymptotically Gaussian random fields, with an application to climate Open
The goal of this paper is to give confidence regions for the excursion set of a spatial function above a given threshold from repeated noisy observations on a fine grid of fixed locations. Given an asymptotically Gaussian estimator of the …