arXiv research

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

New regularization method reduces support of empirical risk minimization solutions.

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

We introduce a pathwise approach to analyze the relative performance of an equity portfolio with respect to a benchmark market portfolio. In this energy-entropy framework, the relative performance is decomposed into three components: a volatility term, a relative entropy term measuring the distance between the portfoli…

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

Study on relative entropy for hypersurfaces in hyperbolic space.

Extends specific relative entropy to multidimensional continuous martingales.

Study uses CSIE to estimate portfolio volatility relative to market.

We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol discretisations of the data. Analysing 1-minute and 5-minute price time series of 55 Exchang…

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

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…

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

The paper generalizes Bayesian Cramér-Rao inequality using information geometry of relative α-entropy.

The notion of utility maximising entropy (u-entropy) of a probability density, which was introduced and studied by Slomczynski and Zastawniak (Ann. Prob 32 (2004) 2261-2285, arXiv:math.PR/0410115 v1), is extended in two directions. First, the relative u-entropy of two probability measures in arbitrary probability space…

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

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…

Quantum ML predicts data with improved speed and accuracy.

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…

New clustering method adapts to data structure.

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…

Entropy analysis via kernel methods for probabilistic inference.

New algorithms for clustering and dimension reduction using relative von Neumann entropy.

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.

Two entropy measures quantify suboptimal portfolio performance.

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…

Paper proves Jeffrey's update rule minimizes relative entropy.

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

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…

Paper introduces a new uncertainty measure for misclassification detection.

REMEDI improves neural entropy estimation across various tasks.

The null energy condition is characterized via convexity of entropy in Lorentzian manifolds.

New bound limits generalization gap for large models, independent of model complexity.

We show that Entropy-SGD (Chaudhari et al., 2017), when viewed as a learning algorithm, optimizes a PAC-Bayes bound on the risk of a Gibbs (posterior) classifier, i.e., a randomized classifier obtained by a risk-sensitive perturbation of the weights of a learned classifier. Entropy-SGD works by optimizing the bound's p…

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 surface area measures defined for ball-convex bodies, leading to entropy and inequalities.

We give several Bishop-Gromov relative volume comparisons with integral Ricci curvature which improve the results in \cite{PW1}. Using one of these volume comparisons, we derive an estimate for the volume entropy in terms of integral Ricci curvature which substantially improves an earlier estimate in \cite{Au2} and giv…

We advocate the use of a notion of entropy that reflects the relative abundances of the symbols in an alphabet, as well as the similarities between them. This concept was originally introduced in theoretical ecology to study the diversity of ecosystems. Based on this notion of entropy, we introduce geometry-aware count…

The paper extends entropy concepts to Monge-Ampère measures with prescribed singularities.

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

New measure of maximal entropy found for a class of geometrically finite groups.

Entropy measure quantifies volatility correlation and risk diversity in asset portfolios.

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

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

This work extends ME-RL using diffusion models to sample optimal policies.

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