A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Optimizes distributions robustly with Sinkhorn distance.
Paper uses Sinkhorn distances to improve imitation learning effectiveness.
The Sinkhorn "distance", a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference. However, the time and memory requirements of standard algorithms for computing this distance grow quadratically with the size of the data, making th…
Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance, it is unknown whether general optimal transport distances can be approximated in …
Study convergence and approximations of entropic regularized Wasserstein distances for Gaussian and RKHS measures.
Paper proves generalized Talagrand inequality for Sinkhorn distance.
Correctly estimating the discrepancy between two data distributions has always been an important task in Machine Learning. Recently, Cuturi proposed the Sinkhorn distance which makes use of an approximate Optimal Transport cost between two distributions as a distance to describe distribution discrepancy. Although it ha…
Paper proposes a robust hypothesis testing method using Sinkhorn distance.
New stability theory for Sinkhorn semigroups with explicit decay rates.
A new method for faster estimation of Wasserstein distance using Sinkhorn divergence.
Improved online Sinkhorn algorithm for large-scale data processing.
Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks. Yet, computing OT distances between arbitrary (i.e. not necessarily discrete) probability distributions remains an open problem. This paper introduces a new online estimator of entropy-regularized OT distances between two such arbitr…
SNS accelerates Sinkhorn algorithm with sparse Newton iterations.
The Sinkhorn flow converges to a Wasserstein mirror gradient flow from the Sinkhorn algorithm.
This paper tackles Sinkhorn DRO by reformulating it as a bilevel program and proposes sampling-based algorithms.
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by a regularized version that is less accurate but easy to differentiate. In this …
We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to screen those components by directly setting them at that value before entering t…
This work studies Gaussian geometry under entropy-regularized 2-Wasserstein distance.
This study approximates distances between Gaussian processes and covariance operators using RKHS.
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation involves the resolution of a linear program whose cost is prohibitive whenever the hi…
New methods improve stability of Sinkhorn algorithm in machine learning.
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been studied in depth: unbalanced transport, which is robust to the presence of outli…
Paper tackles robust model training with a new stochastic algorithm.
New stability bounds for Sinkhorn's algorithm in entropic optimal transport.
Study entropic regularization of Gaussian measures and processes on Hilbert space.
New framework for efficient optimal transport distances between Markov chains.
Paper proposes SinkhornDRL for distributional RL using Sinkhorn divergence and regularized Wasserstein loss.
Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or regularized variations such as Sinkhorn distance. However, as we will demonstrate, regu…
Optimal transport offers an alternative to maximum likelihood for learning generative autoencoding models. We show that minimizing the p-Wasserstein distance between the generator and the true data distribution is equivalent to the unconstrained min-min optimization of the p-Wasserstein distance between the encoder agg…
Introduces new Wasserstein distances for more intrinsic metrics.
Debiased Wasserstein barycenters improve on entropy regularization in OT.
LOT Wassmap speeds up Wasserstein space manifold learning.
The paper studies how different entropic regularizations affect GAN solutions.
SinSim improves self-supervised learning by integrating optimal transport into contrastive learning.
This paper speeds up WMD computation for multiple queries efficiently.
In this report, we review the calculation of entropy-regularised Wasserstein loss introduced by Cuturi and document a practical implementation in PyTorch. Code is available at https://github.com/t-vi/pytorch-tvmisc/blob/master/wasserstein-distance/Pytorch_Wasserstein.ipynb
A rapidly growing area of work has studied the existence of adversarial examples, datapoints which have been perturbed to fool a classifier, but the vast majority of these works have focused primarily on threat models defined by norm-bounded perturbations. In this paper, we propose a new threat model for adver…
We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between discrete probability distributions supported each on support points. First, we show that the standard linear programming (LP) represe…
COT-GAN generates sequential data with a causal optimal transport approach.
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear Discriminant Analysis (LDA), WDA selects the projection matrix that maximizes the …
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics whenever the ground distance between the marginals is a metric, generalize both…
Continuous-time Sinkhorn flow generalizes and unifies existing dynamics.
The Sinkhorn-Knopp derivatives converge with linear rate.
As a fundamental problem of natural language processing, it is important to measure the distance between different documents. Among the existing methods, the Word Mover's Distance (WMD) has shown remarkable success in document semantic matching for its clear physical insight as a parameter-free model. However, WMD is e…
Paper solves barycenter of probability distributions using Sinkhorn divergence.
Survey of Sinkhorn algorithm for optimal transport, emphasizing its geometric origins.
This work studies the statistical performance of Sinkhorn iterations in estimating Schrödinger bridges.
We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most components. We show that the complexity of the Sinkhorn algorithm for finding an -appr…