# Statistical inference with regularized optimal transport

@inproceedings{Goldfeld2022StatisticalIW, title={Statistical inference with regularized optimal transport}, author={Ziv Goldfeld and Kengo Kato and Gabriel Rioux and Ritwik Sadhu}, year={2022} }

. Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suﬀer from computational and statistical scalability issues to high dimensions, which motivated the study of regularized OT methods like slicing, smoothing, and entropic penalty. This work establishes a uniﬁed framework for deriving limit distributions of empirical regularized OT distances, semiparametric e…

## 8 Citations

### Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distances

- Computer ScienceArXiv
- 2022

This work quantifies sliced Wasserstein distances scalability from three key aspects: empirical convergence rates; robustness to data contamination; and efficient computational methods; and characterize minimax optimal, dimension-free robust estimation risks, and show an equivalence between robust 1-Wasserstein estimation and robust mean estimation.

### Distributional Convergence of the Sliced Wasserstein Process

- Computer Science
- 2022

A framework is obtained in which to prove distributional limit results for all Wasserstein distances based on one-dimensional projections and illustrates these results on a number of examples where no distributional limits were previously known.

### Wasserstein Distributionally Robust Optimization via Wasserstein Barycenters

- Computer ScienceArXiv
- 2022

This work proposes constructing the nominal distribution in optimal transport-based distributionally robust optimization problems through the notion of Wasserstein barycenter as an aggregation of data samples from multiple sources and demonstrates that the proposed scheme outperforms other widely used estimators in both the low- and high-dimensional regimes.

### Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters

- Computer Science
- 2022

This work proposes constructing the nominal distribution in optimal transport-based distributionally robust optimization problems through the notion of Wasserstein barycenter as an aggregation of data samples from multiple sources through which it outperforms other widely used estimators in both the low- and high-dimensional regimes.

### Weak limits of entropy regularized Optimal Transport; potentials, plans and divergences

- Mathematics, Computer Science
- 2022

The central limit theorem of the Sinkhorn potentials and the weak limits of the couplings are obtained, proving a conjecture of Harchaoui, Liu and Pal (2020) and enabling statistical inference based on entropic regularized optimal transport.

### Limit distribution theory for f-Divergences

- Mathematics, Computer ScienceArXiv
- 2022

A general methodology for deriving distributional limits for f -divergences based on the functional delta method and Hadamard directional differentiability is developed and an application of the limit distribution theory to auditing differential privacy is proposed and analyzed for significance level and power against local alternatives.

### Central limit theorem for the Sliced 1-Wasserstein distance and the max-Sliced 1-Wasserstein distance

- Computer Science
- 2022

This paper utilizes the central limit theorem in Banach space to derive the limit distribution for the Sliced 1-Wasserstein distance and proves that the function class is P -Donsker under mild moment assumption and investigates how many random projections can make sure the error small in high probability.

### Martingale Methods for Sequential Estimation of Convex Functionals and Divergences

- Mathematics, Computer Science
- 2021

An offline-to-sequential device is constructed that converts a wide array of existing offline concentration inequalities into time-uniform confidence sequences that can be continuously monitored, providing valid tests or confidence intervals at arbitrary stopping times.

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