arXiv Statistics ML
Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testing
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arXiv Machine Learning
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Distributionally Robust Optimization via Iterative Algorithms in Continuous Probability Spaces
arXiv:2412. 20556v2 Announce Type: replace-cross Abstract: We study distributionally robust optimization (DRO) for robust inference when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem.
arXiv Statistics ML
Sep 28
Brenier Meets Adversarial Training: Optimal Transport Geometry for Robust Learning
The paper introduces a penalized distributionally robust optimization framework that allows an adversary to choose any distribution while incurring a Wasserstein penalty for deviating from the empirical distribution. It shows that the adversary’s problem can be reformulated as optimizing transport maps that push empirical samples to adversarial ones, proving that optimal maps are cyclically monotone. The authors argue that standard per-sample adversarial training violates this property and propose two remedies—multi-start particle ascent and input-convex neural network parameterization—to enforce cyclical monotonicity, demonstrating improved robustness and generalization in experiments on regression, image classification, and control tasks.
arXiv AI
Sep 10
Deep Barycentric Regression for Optimal Transport Map Estimation and its Statistical Optimality
The paper introduces BROT, a two‑step approach for estimating optimal transport maps. First, it computes the unregularized OT plan, then fits a deep neural network to the resulting barycentric targets using least‑squares regression. The authors prove that, under standard regularity conditions, BROT achieves the minimax convergence rate when the true OT map is Lipschitz, and demonstrate its effectiveness on synthetic data, images, and downstream tasks such as single‑cell perturbation prediction and unsupervised domain adaptation.
arXiv Machine Learning
Aug 13
A Local Sinkhorn Framework for Conditional Distribution Reconstruction of Multidimensional Random Fields
arXiv:2608. 11613v1 Announce Type: new Abstract: In this paper, we propose a local Sinkhorn divergence framework for conditional distribution reconstruction of multidimensional random fields.
arXiv Machine Learning
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Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows
arXiv:2608. 11544v1 Announce Type: cross Abstract: We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics.
arXiv Machine Learning
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Wasserstein Filtering: A Sample Selection Method for Robust Distribution Learning
arXiv:2608. 13418v1 Announce Type: cross Abstract: Given a dataset where a portion of the samples are contaminated, our goal is to recover the underlying clean population distribution.