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.
LogDet estimator improves entropy estimation in neural networks.
Numerically estimates Colding-Minicozzi entropies of self-shrinkers.
REMEDI improves neural entropy estimation across various tasks.
New algorithm estimates semi-continuous data density using entropy maximization.
AR-DAE approximates entropy gradient for machine learning models.
Optimal geometric estimates for Kähler manifolds with bounded Nash entropy
The intrinsic entropy model accurately estimates stock market volatility.
The paper corrects biases in estimating intrinsic dimension and differential entropy.
New estimator for joint entropy outperforms existing methods in various distributions.
A neural network method estimates entropy production from system trajectories.
Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be carried out without explicit background noise characterization. However, state of…
The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such appr…
Paper proposes a policy-search algorithm to learn entropy-maximizing exploration policies in reward-free environments.
Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic quantities as test statistics, that is, as quantities obtained from empirical data, p…
New methods for inferring, predicting, and estimating continuous-time, discrete-event processes.
ALIEN improves uncertainty estimation of language models by refining entropy-based methods.
In this survey we review Hamilton's entropy and Perelman's entropy, and provide motivations for these concepts. Then we review recent results on the logarithmic Sobolev inequality, the Sobolev inequalities and kappa-noncollapsing estimates along the Ricci flow, including the Ricci flow with surgeries.
Estimating the entropy based on data is one of the prototypical problems in distribution property testing and estimation. For estimating the Shannon entropy of a distribution on elements with independent samples, [Paninski2004] showed that the sample complexity is sublinear in , and [Valiant--Valiant2011] showed…
This note relaxes conditions for Kähler metrics with bounded entropy and scalar curvature.
In this note, we obtain the asymptotic estimate for the time derivative of the -entropy in terms of the lower bound on the Bakry-Emery curvature. In the cases of Hyperbolic space and Heisenberg group, we show that the time derivative of the -entropy is non-increasing, and we also get sharp asymptotic bound …
We present a procedure for effective estimation of entropy and mutual information from small-sample data, and apply it to the problem of inferring high-dimensional gene association networks. Specifically, we develop a James-Stein-type shrinkage estimator, resulting in a procedure that is highly efficient statistically …
We consider the entropy of the solution to the heat equation on a Riemannian manifold. When the manifold is compact, we provide two estimates on the rate of change of the entropy in terms of the lower bound on the Ricci curvature and the spectral gap respectively. Our explicit computation for the three dimensional hype…
The paper establishes sub-gradient estimates and entropy formulas for quaternionic contact geometry heat equations.
Improved machine learning method estimates entropy production robustly.
The paper studies practical estimation and interpretation of Rényi transfer entropy.
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically, profile entropy a) determines the speed of estimating the distribution relative t…
We study volume growth, entropy and stability for translating solitons of mean curvature flow. First, we prove that every complete properly immersed translator has at least linear volume growth. Then, by using Huisken's monotonicity formula, we compute the entropy of the grim reaper and the bowl solitons. We also give …
Paper tests for time-varying entropy in stock prices, finding periods of inefficiency.
New method estimates robust multi-period portfolios using entropy.
We extend the notion of the geometric entropy of foliation to foliated manifolds equipped with leafwise Finsler structure. We study the relation between the geometric entropy and the topological entropy of the holonomy pseudogroup. The case of foliated manifold with leafwise Randers structure. In this case the estimate…
Study Transformer layers under cross-entropy training using mean field control.
We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from standard maximum likelihood estimation.We demonstrate the LME principle BY deriving …
The paper proves lower bounds for Gaussian-weighted curvature integrals of self-shrinkers.
Estimates Kähler metric diameters with entropy bound alone.
In this paper, we prove Perelman type -entropy formulae and global differential Harnack estimates for positive solutions to porous medium equation on the closed Riemannian manifolds with Ricci curvature bounded below. As applications, we derive Harnack inequalities and Laplacian estimates.
The maximum entropy principle can be used to assign utility values when only partial information is available about the decision maker's preferences. In order to obtain such utility values it is necessary to establish an analogy between probability and utility through the notion of a utility density function. According…
The relative -entropy is the Rényi analog of relative entropy and arises prominently in information-theoretic problems. Recent information geometric investigations on this quantity have enabled the generalization of the Cramér-Rao inequality, which provides a lower bound for the variance of an estimator of an escort…
Entrocraft addresses RL performance saturation in LLMs by customizing entropy curves.
Paper presents estimators for entropy and information in probabilistic models.
Accounting for the non-normality of asset returns remains challenging in robust portfolio optimization. In this article, we tackle this problem by assessing the risk of the portfolio through the "amount of randomness" conveyed by its returns. We achieve this by using an objective function that relies on the exponential…
Estimate relaxation times in nonextensive systems using gradient flow for Tsallis entropy maximization.
If pricing kernels are assumed non-negative then the inverse problem of finding the pricing kernel is well-posed. The constrained least squares method provides a consistent estimate of the pricing kernel. When the data are limited, a new method is suggested: relaxed maximization of the relative entropy. This estimator …
Uniform Sobolev inequality for Kähler metrics with entropy bound.
We approximate differential entropy for efficient Bayesian experimental design.
Compressed Counting (CC) [22] was recently proposed for estimating the ath frequency moments of data streams, where 0 < a <= 2. CC can be used for estimating Shannon entropy, which can be approximated by certain functions of the ath frequency moments as a -> 1. Monitoring Shannon entropy for anomaly detection (e.g., DD…
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…
Causal discovery is a fundamental problem in statistics and has wide applications in different fields. Transfer Entropy (TE) is a important notion defined for measuring causality, which is essentially conditional Mutual Information (MI). Copula Entropy (CE) is a theory on measurement of statistical independence and is …
Proposes a new method to measure epistemic uncertainty in Bayesian neural networks.