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.
Inference for normal and Monte Carlo distributions using minimum relative entropy.
A measure called relative cluster entropy distinguishes between correlated and uncorrelated sequences.
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…
We consider the problem of identifying the causal direction between two discrete random variables using observational data. Unlike previous work, we keep the most general functional model but make an assumption on the unobserved exogenous variable: Inspired by Occam's razor, we assume that the exogenous variable is sim…
Study on Bayesian reinforcement learning performance bounds.
Paper compares two entropy concepts for finite presentation groups.
We study the problem of finding probability densities that match given European call option prices. To allow prior information about such a density to be taken into account, we generalise the algorithm presented in Neri and Schneider (2011) to find the maximum entropy density of an asset price to the relative entropy c…
Proposes a method to solve deep neural networks' local minimum problem.
Study on relative entropy for hypersurfaces in hyperbolic space.
We study the problem of identifying the causal relationship between two discrete random variables from observational data. We recently proposed a novel framework called entropic causality that works in a very general functional model but makes the assumption that the unobserved exogenous variable has small entropy in t…
Exponential models of distributions are widely used in machine learning for classiffication and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we argue that for classiffication tasks, mutual information is a more suitable informa…
The study finds the minimum average area ratio on hyperbolic manifolds and its relation to scalar curvature.
Extends specific relative entropy to multidimensional continuous martingales.
Entropy asymmetry affects regularization in ERM, leading to biased solutions.
In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned function to approximate the minimum error entropy, is shown to be always true if the…
Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corre…
Entropy measure quantifies volatility correlation and risk diversity in asset portfolios.
We derive generalization and excess risk bounds for neural nets using a family of complexity measures based on a multilevel relative entropy. The bounds are obtained by introducing the notion of generated hierarchical coverings of neural nets and by using the technique of chaining mutual information introduced in Asadi…
New method uncovers zero entropy in dependent observations after finite samples.
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…
This essay quantifies convexities in incomplete markets using entropy, adjusting prices for risk and incompleteness.
New statistical test for change-point detection using 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…
New regularization method reduces support of empirical risk minimization solutions.
The entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems. We develop the minimum entropy density method (MEDM) to detect the structure scale of a given time series, which is defined as the scale in which the uncertainty is minimized, hence the p…
Researchers explore gauge freedom in entropies of -Gaussian measures.
Paper proposes deep neural networks for nonparametric regression from dependent data.
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…
We investigate the -relative entropy, which stems from the Bregman divergence, on weighted Riemannian and Finsler manifolds. We prove that the displacement -convexity of the -relative entropy is equivalent to the combination of the nonnegativity of the weighted Ricci curvature and the -convexity of the weig…
The study improves representation learning bounds using data-dependent Gaussian mixtures.
We consider the minimum error entropy (MEE) criterion and an empirical risk minimization learning algorithm in a regression setting. A learning theory approach is presented for this MEE algorithm and explicit error bounds are provided in terms of the approximation ability and capacity of the involved hypothesis space w…
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…
Efficiently constructs sparse ROMs for high-dimensional data using causation entropy.
Entropy analysis via kernel methods for probabilistic inference.
The entropy of minimal surfaces is minimized in hyperbolic manifolds.
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…
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…
Paper proves Jeffrey's update rule minimizes relative entropy.
Consider the problem of estimating the minimum entropy of pseudo-Anosov maps on a surface of genus with punctures. We determine the behaviour of this minimum number for a certain large subset of the plane, up to a multiplicative constant. In particular it has been shown that for fixed , this minimum …
A new method, REC, compresses images by encoding their latent representations efficiently.
Abstract: Necessary and sufficient conditions for gradient flows of relative entropy in Lindblad equations.
Comparing with traditional learning criteria, such as mean square error (MSE), the minimum error entropy (MEE) criterion is superior in nonlinear and non-Gaussian signal processing and machine learning. The argument of the logarithm in Renyis entropy estimator, called information potential (IP), is a popular MEE cost i…
The minimum error entropy (MEE) criterion has been verified as a powerful approach for non-Gaussian signal processing and robust machine learning. However, the implementation of MEE on robust classification is rather a vacancy in the literature. The original MEE only focuses on minimizing the Renyi's quadratic entropy …