arXiv research

Formula derived for curvature in measure spaces.

Unified framework for analyzing gradient flows of measures with exponential decay of entropy.

A new associative memory uses Sinkhorn divergence for efficient pattern retrieval.

This work develops sampling methods for differential privacy using SHK geometry.

This paper uses UOT metrics for better dimensionality reduction and classification/clustering.

The study analyzes the evolution of Gaussian measures under a specific gradient flow.

New stability theory for Sinkhorn semigroups with explicit decay rates.

Private minimum Hellinger distance estimators maintain robustness and efficiency while ensuring privacy.

A new algorithm for better decision-making in recommendation systems.

This thesis uses Kantorovich-Rubinstein distance for classifying points based on their measures.

Robust test for distributions under Hellinger distance, simpler than optimal tests.

This paper studies neural network operators and their convergence properties.

Sharp inequality between TV and Hellinger distances for Gaussian mixtures.

Study robust hypothesis testing under Hellinger distance, proving lower bounds and providing tests.

Constructs portfolios based on Hellinger distance to normal, finding market invariance.

New f-Betas for portfolio optimization using f-divergence risk measures.

Proposes a variational NNCC formulation for infinite dimensions.

Optimal transport adapted for contaminated probabilities, showing equivalence under specific conditions.

Geometric analysis on diffeomorphism groups for fluid dynamics and information geometry.

Proposes new loss functions for GANs to improve estimation accuracy and robustness.

Study optimal transport on globally hyperbolic spacetimes, focusing on weak Kantorovich potentials' regularity.

Enhances SDR via Hellinger correlation for better data dependency understanding.

The paper is accompanying "A general Duality Theorem for the Monge-Kantorovich Transport Problem". We explain the methods used in this article in an elementary setting and present two examples complementing the results obtained therein.

We refine and generalize several interpolation inequalities bounding the $L^p$ norm of a probability density with respect to the reference measure $μ$ by its Sobolev norm and the Kantorovich distance to $μ$ on a smooth weighted Riemannian manifold satisfying $CD(0, \infty)$ condition.

Unified approach solves Kyle model with dynamic information.

Proves uniqueness of barycenters on manifolds without restrictions.

This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance between a pair of $d$-dimensional histograms having $n$ bins each. We prove that this problem is equivalent to an uncapacitated minimum cost flow problem on a $(d+1)$-partite graph with $(d+1)n$ nodes and $dn^{\frac{d+1}{d}}$ arcs,…

Optimizes angular velocity transfers for rigid bodies under deadline constraints.

Unified framework for model-based RL with sample complexity guarantees.

Revisits shallow neural networks using Lipschitz norms and measures.

Classifiers trained on data sets possessing an imbalanced class distribution are known to exhibit poor generalisation performance. This is known as the imbalanced learning problem. The problem becomes particularly acute when we consider incremental classifiers operating on imbalanced data streams, especially when the l…

New method calculates cut locus on Riemannian manifolds using optimal transport.

New method improves learning from multiple correlated data trajectories.

The subject of this article is the introduction of a new concept of well-posedness of Bayesian inverse problems. The conventional concept of (Lipschitz, Hellinger) well-posedness in [Stuart 2010, Acta Numerica 19, pp. 451-559] is difficult to verify in practice and may be inappropriate in some contexts. Our concept sim…

Unified Kantorovich duality for multimarginal optimal transport on Polish spaces.

The paper establishes general results in Lorentzian optimal transport theory.

New framework for optimal transport with jumps over intermediate spaces.

In reinforcement learning (RL), temporal abstraction still remains as an important and unsolved problem. The options framework provided clues to temporal abstraction in the RL, and the option-critic architecture elegantly solved the two problems of finding options and learning RL agents in an end-to-end manner. However…

We show that the square Hellinger distance between two Bayesian networks on the same directed graph, $G$, is subadditive with respect to the neighborhoods of $G$. Namely, if $P$ and $Q$ are the probability distributions defined by two Bayesian networks on the same DAG, our inequality states that the square Hellinger di…

New algorithm for estimating multivariate quantiles using stochastic optimal transport.

Study sharp convergence rates of empirical UOT for spatio-temporal point processes.

This paper deals with forward performances of HARA type. Precisely, for a market model in which stock price processes are modeled by a locally bounded $d$-dimensional semimartingale, we elaborate a complete and explicit characterization for this type of forward utilities. Furthermore, the optimal portfolios for each of…

Paper proposes a new method for density estimation using squared Hellinger distance.

Efficiently predicts optimal transport plans using sliced potentials.

Paper derives convergence rates for NPMLE in Hellinger distance using deep neural networks.

A general duality proof for Wasserstein distributionally robust optimization.

In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes. This leads to a geometric interpretation to generative models, and leads to a novel …

New algorithm for linear bandits tackles Optimal Transport problems.