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Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…

Statistics Theory · Mathematics 2018-10-03 Jonathan H. Huggins , Trevor Campbell , Mikołaj Kasprzak , Tamara Broderick

Recent advances in generative models highlight the power of geometry-aware modeling in manifold-constrained settings. Yet, for natural images, the field remains confined to Euclidean assumptions, failing to exploit the potential of…

Computer Vision and Pattern Recognition · Computer Science 2026-05-26 Junho Lee , Kwanseok Kim , Joonseok Lee

In this paper, we propose a class of non-parametric classifiers, that learn arbitrary boundaries and generalize well. Our approach is based on a novel way to regularize 1NN classifiers using a greedy approach. We refer to this class of…

Machine Learning · Computer Science 2024-02-14 Aditya Challa , Sravan Danda , Laurent Najman

We study the quantitative convergence of drift-diffusion PDEs that arise as Wasserstein gradient flows of linearly convex functions over the space of probability measures on ${\mathbb R}^d$. In this setting, the objective is in general not…

Optimization and Control · Mathematics 2025-07-17 Lénaïc Chizat , Maria Colombo , Xavier Fernández-Real

One of the most popular approaches for solving total variation-regularized optimization problems in the space of measures are Particle Gradient Flows (PGFs). These restrict the problem to linear combinations of Dirac deltas and then perform…

Optimization and Control · Mathematics 2026-03-31 Christian Amend , Marcello Carioni , Konstantinos Zemas

Optimization over the space of probability measures endowed with the Wasserstein-2 geometry is central to modern machine learning and mean-field modeling. However, traditional methods relying on full Wasserstein gradients often suffer from…

Machine Learning · Statistics 2026-04-03 Yewei Xu , Qin Li

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

We provide a numerical analysis and computation of neural network projected schemes for approximating one dimensional Wasserstein gradient flows. We approximate the Lagrangian mapping functions of gradient flows by the class of two-layer…

Numerical Analysis · Mathematics 2024-02-27 Xinzhe Zuo , Jiaxi Zhao , Shu Liu , Stanley Osher , Wuchen Li

We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can…

Machine Learning · Computer Science 2025-05-28 Simon Dirmeier , Antonietta Mira

Transport maps can ease the sampling of distributions with non-trivial geometries by transforming them into distributions that are easier to handle. The potential of this approach has risen with the development of Normalizing Flows (NF)…

Machine Learning · Statistics 2024-02-20 Louis Grenioux , Alain Durmus , Éric Moulines , Marylou Gabrié

With the rapidly growing model complexity and data volume, training deep generative models (DGMs) for better performance has becoming an increasingly more important challenge. Previous research on this problem has mainly focused on…

Machine Learning · Computer Science 2021-12-08 Yufan Zhou , Chunyuan Li , Changyou Chen , Jinhui Xu

Normalizing Flows (NFs) are universal density estimators based on Neural Networks. However, this universality is limited: the density's support needs to be diffeomorphic to a Euclidean space. In this paper, we propose a novel method to…

Machine Learning · Computer Science 2022-02-02 Christian Horvat , Jean-Pascal Pfister

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…

Tabular regression is a well-studied problem with numerous industrial applications, yet most existing approaches focus on point estimation, often leading to overconfident predictions. This issue is particularly critical in industrial…

Likelihood-based deep generative models have been widely investigated for Image Anomaly Detection (IAD), particularly Normalizing Flows, yet their strict architectural invertibility needs often constrain scalability, particularly in…

Computer Vision and Pattern Recognition · Computer Science 2026-04-15 Liangwei Li , Lin Liu , Hanzhe Liang , Juanxiu Liu , Jing Zhang , Ruqian Hao , Xiaohui Du , Yong Liu , Pan Li

A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…

Machine Learning · Statistics 2026-02-24 Yinan Hu , Esteban G. Tabak

Particle-based variational inference methods (ParVIs) such as Stein variational gradient descent (SVGD) update the particles based on the kernelized Wasserstein gradient flow for the Kullback-Leibler (KL) divergence. However, the design of…

Machine Learning · Statistics 2023-10-26 Ziheng Cheng , Shiyue Zhang , Longlin Yu , Cheng Zhang

In order to sample from an unnormalized probability density function, we propose to combine continuous normalizing flows (CNFs) with rejection-resampling steps based on importance weights. We relate the iterative training of CNFs with…

Machine Learning · Statistics 2025-08-14 Johannes Hertrich , Robert Gruhlke

Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…

Machine Learning · Computer Science 2023-12-06 Ryoma Yataka , Kazuki Hirashima , Masashi Shiraishi

We present a framework for Nesterov's accelerated gradient flows in probability space to design efficient mean-field Markov chain Monte Carlo (MCMC) algorithms for Bayesian inverse problems. Here four examples of information metrics are…

Optimization and Control · Mathematics 2022-06-27 Yifei Wang , Wuchen Li