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We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show…

Optimization and Control · Mathematics 2026-05-27 Zusen Xu , Jia-Jie Zhu

Wasserstein gradient flows provide a powerful means of understanding and solving many diffusion equations. Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over…

Machine Learning · Computer Science 2021-10-26 Petr Mokrov , Alexander Korotin , Lingxiao Li , Aude Genevay , Justin Solomon , Evgeny Burnaev

Language models are prone to dataset biases, known as shortcuts and spurious correlations in data, which often result in performance drop on new data. We present a new debiasing framework called ``FairFlow'' that mitigates dataset biases by…

Machine Learning · Computer Science 2025-03-25 Jiali Cheng , Hadi Amiri

We study estimation problems in safety-critical applications with streaming data. Since estimation problems can be posed as optimization problems in the probability space, we devise a stochastic projected Wasserstein gradient flow that…

Systems and Control · Electrical Eng. & Systems 2023-04-07 Nicolas Lanzetti , Efe C. Balta , Dominic Liao-McPherson , Florian Dörfler

Many machine learning problems can be seen as approximating a \textit{target} distribution using a \textit{particle} distribution by minimizing their statistical discrepancy. Wasserstein Gradient Flow can move particles along a path that…

Machine Learning · Statistics 2024-06-07 Song Liu , Jiahao Yu , Jack Simons , Mingxuan Yi , Mark Beaumont

In this work, we introduce a novel framework for privately optimizing objectives that rely on Wasserstein distances between data-dependent empirical measures. Our main theoretical contribution is, based on an explicit formulation of the…

Machine Learning · Computer Science 2025-05-22 David Rodríguez-Vítores , Clément Lalanne , Jean-Michel Loubes

Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…

Machine Learning · Statistics 2024-03-12 Yifan Chen , Daniel Zhengyu Huang , Jiaoyang Huang , Sebastian Reich , Andrew M Stuart

It is well known that deep generative models have a rich latent space, and that it is possible to smoothly manipulate their outputs by traversing this latent space. Recently, architectures have emerged that allow for more complex…

Machine Learning · Computer Science 2019-12-06 Andrew Gambardella , Atılım Güneş Baydin , Philip H. S. Torr

Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…

Methodology · Statistics 2022-09-13 Chengliang Tang , Nathan Lenssen , Ying Wei , Tian Zheng

Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…

Machine Learning · Computer Science 2026-03-27 Chandan Tankala , Dheeraj M. Nagaraj , Anant Raj

Unsupervised models can provide supplementary soft constraints to help classify new target data under the assumption that similar objects in the target set are more likely to share the same class label. Such models can also help detect…

Machine Learning · Computer Science 2015-03-13 Ayan Acharya , Eduardo R. Hruschka , Joydeep Ghosh , Badrul Sarwar , Jean-David Ruvini

The performance of machine learning (ML) models critically depends on the quality and representativeness of the training data. In applications with multiple heterogeneous data generating sources, standard ML methods often learn spurious…

Diffusion models and flow-based methods have shown impressive generative capability, especially for images, but their sampling is expensive because it requires many iterative updates. We introduce W-Flow, a framework for training a…

Machine Learning · Computer Science 2026-05-28 Jiaqi Han , Puheng Li , Qiushan Guo , Renyuan Xu , Stefano Ermon , Emmanuel J. Candès

Wasserstein gradient flows are continuous time dynamics that define curves of steepest descent to minimize an objective function over the space of probability measures (i.e., the Wasserstein space). This objective is typically a divergence…

Optimization and Control · Mathematics 2021-02-23 Adil Salim , Anna Korba , Giulia Luise

Investigation of machine learning algorithms robust to changes between the training and test distributions is an active area of research. In this paper we explore a special type of dataset shift which we call class-dependent domain shift.…

Machine Learning · Computer Science 2020-07-13 Tigran Galstyan , Hrant Khachatrian , Greg Ver Steeg , Aram Galstyan

We study the convergence of gradient flow for the training of deep neural networks. If Residual Neural Networks are a popular example of very deep architectures, their training constitutes a challenging optimization problem due notably to…

Machine Learning · Computer Science 2025-07-22 Raphaël Barboni , Gabriel Peyré , François-Xavier Vialard

In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning…

Machine Learning · Statistics 2023-06-28 Shanshan Song , Tong Wang , Guohao Shen , Yuanyuan Lin , Jian Huang

We introduce manifold-learning flows (M-flows), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs,…

Machine Learning · Statistics 2020-11-16 Johann Brehmer , Kyle Cranmer

Discrete flow-based models are a recently proposed class of generative models that learn invertible transformations for discrete random variables. Since they do not require data dequantization and maximize an exact likelihood objective,…

Machine Learning · Computer Science 2021-07-27 Alexandra Lindt , Emiel Hoogeboom

Machine learning systems must adapt to data distributions that evolve over time, in applications ranging from sensor networks and self-driving car perception modules to brain-machine interfaces. We consider gradual domain adaptation, where…

Machine Learning · Computer Science 2020-02-27 Ananya Kumar , Tengyu Ma , Percy Liang