arXiv research

Study on relative entropy for hypersurfaces in hyperbolic space.

Extends specific relative entropy to multidimensional continuous martingales.

New statistical test for change-point detection using relative entropy.

Inference for normal and Monte Carlo distributions using minimum relative entropy.

Entropy asymmetry affects regularization in ERM, leading to biased solutions.

New regularization method reduces support of empirical risk minimization solutions.

We investigate the $m$-relative entropy, which stems from the Bregman divergence, on weighted Riemannian and Finsler manifolds. We prove that the displacement $K$-convexity of the $m$-relative entropy is equivalent to the combination of the nonnegativity of the weighted Ricci curvature and the $K$-convexity of the weig…

We define a relative entropy for two expanding solutions to mean curvature flow of hypersurfaces, asymptotic to the same cone at infinity. Adapting work of White and using recent results of Bernstein and Bernstein-Wang, we show that expanders with vanishing relative entropy are unique in a generic sense. This also impl…

Unique continuation result for expanding Ricci solitons.

We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler manifold. We prove that the convexity of all the entropies in this class is equivalent to the combination of the nonnegative weighted Ricci cur…

Study quantifies information flow in neural networks using relative entropy and RG analogy.

This paper optimizes trading strategies to minimize risk and maximize profit while accounting for market uncertainty.

Paper proves Jeffrey's update rule minimizes relative entropy.

A new method, REC, compresses images by encoding their latent representations efficiently.

In this paper we focus on the uniqueness question for (expanding) solutions of the Harmonic map flow coming out of smooth 0-homogeneous maps with values into a closed Riemannian manifold. We introduce a relative entropy for two purposes. On the one hand, we prove the existence of two expanding solutions associated to a…

Earlier studies have shown that stock market distributions can be well described by distributions derived from Tsallis entropy, which is a generalization of Shannon entropy to non-extensive systems. In this paper, Tsallis relative entropy (TRE), which is the generalization of Kullback-Leibler relative entropy (KLRE) to…

This paper strengthens the central limit theorem for order statistics using relative entropy.

Abstract: Necessary and sufficient conditions for gradient flows of relative entropy in Lindblad equations.

Paper develops a robust HVA measure for dynamic hedging under liquidity stress.

Mathematical analysis of SNE and t-SNE for dimension reduction.

Researchers explore gauge freedom in entropies of $q$-Gaussian measures.

This work tightens generalization error bounds using Wasserstein distance.

REGS samples from unnormalized distributions using gradient flow and neural networks.

This paper uses normalizing flows to approximate transport maps between densities.

In his 2011 work, Maas has shown that the law of any time-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. In this work we show the converse to the above by showing that if the relative law of a Markov chain…

New method uses asymmetric Tsallis relative entropy for better risk assessment in financial portfolios.

The study optimizes distribution estimation from samples with relative entropy error, adapting to sparse distributions.

We study a notion of relative entropy motivated by self-expanders of mean curvature flow. In particular, we obtain the existence of this quantity for arbitrary hypersurfaces trapped between two disjoint self-expanders asymptotic to the same cone. This allows us to begin to develop the variational theory for the relativ…

Entropy analysis via kernel methods for probabilistic inference.

Two entropy measures quantify suboptimal portfolio performance.

Study shows uniform-time chaos propagation in mean field Langevin dynamics.

Study finds optimal martingale coupling between two distributions with minimal entropy.

Kim-Milman flow map stable under regular target measures

A pricing principle is introduced for non-attainable claims in incomplete markets.

This work bounds the generalization error of private algorithms for discrete data.

The goal of this paper is to explore the basic Approximate Bayesian Computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or intractable, but one can simulate from it. We use relative entropy ideas to analyze the beh…

Quantum ML predicts data with improved speed and accuracy.

Improved sampling from complex distributions with reduced bias.

The paper studies harmonic map heat flow to flat tori, proving ergodic behavior and convergence to hyperbolic measure.

Develops a robust hedging valuation adjustment measure for dynamic hedging under liquidity-demand stress.

Paper finds a new principle for optimizing consumption and wealth using Tsallis entropy.

The paper studies scaling limits of hedging prices in financial models.

Econophysics, is based on the premise that some ideas and methods from physics can be applied to economic situations. We intend to show in this paper how a physics concept such as entropy can be applied to an economic problem. In so doing, we demonstrate how information in the form of observable data and moment constra…

We present a derivation of the Kullback Leibler (KL)-Divergence (also known as Relative Entropy) for the von Mises Fisher (VMF) Distribution in $d$-dimensions.

Study proves uniqueness of corrugated negatively curved immersions in differential geometry.

A measure called relative cluster entropy distinguishes between correlated and uncorrelated sequences.

Study shows how optimal transport behaves in higher dimensions.

A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences include many classical information divergence measures, such as relative entropy a…