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.
Study non-Gaussian measures' concentration properties in metric spaces.
Let $L=\DD+Z$ for a vector field on a complete Riemannian manifold possibly with a boundary. By using the uniform distance, a number of transportation-cost inequalities on the path space for the (reflecting) -diffusion process are proved to be equivalent to the curvature condition $\Ric-\nn Z\ge - K$ and t…
Paper introduces information-constrained optimal transport, generalizing Talagrand's inequality.
Starting from a sequence of independent Wright-Fisher diffusion processes on , we construct a class of reversible infinite dimensional diffusion processes on $\DD_\infty:= \{{\bf x}\in Let $Mμ\ff 1 2\DD+ZZ$…
Paper tackles unknown variances in best-arm identification.
We derive weighted log-Sobolev inequalities from a class of super Poincaré inequalities. As an application, the Talagrand inequality with larger distances are obtained. In particular, on a complete connected Riemannian manifold, we prove that the $\log^\dd$-Sobolev inequality with $\dd\in (1,2)$ implies the $L^{2/(2-\d…
Inequalities linking entropy, Fisher info, Stein discrepancy, and Wasserstein distance on Riemannian manifolds.
The paper develops methods for novelty detection on path space using signature-based statistics.
Sharp 2-Wasserstein bounds for DDPMs derived from Föllmer process.
New algorithm clusters Gaussian mixtures with unknown covariance efficiently.
New geometry for optimal transport cost based on Bregman divergences.
Models of spatial firm competition assume that customers are distributed in space and transportation costs are associated with their purchases of products from a small number of firms that are also placed at definite locations. It has been long known that the competition equilibrium is not guaranteed to exist if the mo…
A new method for optimal transport using neural ODEs that preserves marginal constraints.
Study optimal transport for robust optimization, showing how adversary's strategy relates to regularization.
Unified technique for sequential estimation of convex divergences.
With this work we try to analyse the agglomeration process in the Portuguese regions, using the New Economic Geography models. In these models the base idea is that where has increasing returns to scale in the manufactured industry and low transport costs, there is agglomeration. Of referring, as summary conclusion, th…
Based on a study of the coupling by reflection of diffusion processes, a new monotonicity in time of a time-dependent transportation cost between heat distribution is shown under Bakry-Emery's curvature-dimension condition on a Riemannian manifold. The cost function comes from the total variation between heat distribut…
In this paper, it is shown that the reduced -cohomology is trivial for a class of finitely generated amenable groups called transport amenable. These groups are those for which there exist a sequence of measures converging to a left-invariant mean and such that the transport cost between displaced b…
Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient at each iteration. This modest change allows SGLD to escape local minima and suffices to guarantee asymptotic convergence to g…
This manuscript presents some new impossibility results on adversarial robustness in machine learning, a very important yet largely open problem. We show that if conditioned on a class label the data distribution satisfies the Talagrand transportation-cost inequality (for example, this condition is satisfied if t…
We address the problem of defining a network graph on a large collection of classes. Each class is comprised of a collection of data points, sampled in a non i.i.d. way, from some unknown underlying distribution. The application we consider in this paper is a large scale high dimensional survey of people living in the …
We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs, where the Euclidean distance is used, this new method allows …
Paper proposes a new method for regression using optimal transport cost optimization.
Generalised regularisation equals robustness for exotic function classes.
New framework uses PDE for no-regret generative modeling.
Paper introduces a neural network for consistent estimation of optimal transport maps.
Exact generalization guarantees for robust models using Wasserstein distance are established.
Develops bounds predicting deep learning generalization using optimal transport.
New findings on optimal transport gradient for generative models, addressing numerical instabilities.
New methods improve stability of Sinkhorn algorithm in machine learning.
Proposes using Wasserstein barycenter for better multilingual alignment.
Improved BAI under DP reduces gap to constant.
Domain Translation is the problem of finding a meaningful correspondence between two domains. Since in a majority of settings paired supervision is not available, much work focuses on Unsupervised Domain Translation (UDT) where data samples from each domain are unpaired. Following the seminal work of CycleGAN for UDT, …
Given a transportation cost , optimal maps minimize the total cost of moving masses from to . We find a pseudo-metric and a calibration form on such that the graph of an optimal map is a calibrated maximal submanifold. We define the mass of space-like current…
Learning to align multiple datasets is an important problem with many applications, and it is especially useful when we need to integrate multiple experiments or correct for confounding. Optimal transport (OT) is a principled approach to align datasets, but a key challenge in applying OT is that we need to specify a tr…
While progress has been made in understanding the robustness of machine learning classifiers to test-time adversaries (evasion attacks), fundamental questions remain unresolved. In this paper, we use optimal transport to characterize the minimum possible loss in an adversarial classification scenario. In this setting, …
We derive upper bounds on the generalization error of learning algorithms based on their \emph{algorithmic transport cost}: the expected Wasserstein distance between the output hypothesis and the output hypothesis conditioned on an input example. The bounds provide a novel approach to study the generalization of learni…
This paper explores how entropic regularization improves Wasserstein estimators' performance.
We show that on a manifold whose Riemannian metric evolves under backwards Ricci flow two Brownian motions can be coupled in such a way that the expectation of their normalized L-distance is non-increasing. As an immediate corollary we obtain a new proof of a recent result of Topping (J. reine angew. Math. 636 (2009), …
Study matches two noisy point clouds with geometric transformations and relabeling.
Optimizes distributions robustly with Sinkhorn distance.
Study on convergence rates for optimal transport with regularization.
Study dynamic risk measures with distributional uncertainty using optimal transport.
Optimizes resource allocation in a network with random job requests.
The aim of this paper is to analyze the relationship between inter-industry, intra-industry and inter-regional clustering and demand for labor by companies in Portugal. Is expected at the outset that there is more demand for work where the agglomeration is greater. It should be noted, as a summary conclusion, the resul…
This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well …
The goal of the paper is to give an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmological constant and the energy-momentum tensor. Such an optimal transport formulation is in terms of convexity/concavity properties of the …
We investigate and provide new insights on the sampling rule called Top-Two Thompson Sampling (TTTS). In particular, we justify its use for fixed-confidence best-arm identification. We further propose a variant of TTTS called Top-Two Transportation Cost (T3C), which disposes of the computational burden of TTTS. As our …