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.
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…
In this paper, we prove the concavity of the Renyi entropy power for nonlinear diffusion equation (NLDE) associated with the Laplacian and the Witten Laplacian on compact Riemannian manifolds with non-negative Ricci curvature or -condition and on compact manifolds equipped with time dependent metrics and poten…
This is full length article (draft version) where problem number of topics in Topic Modeling is discussed. We proposed idea that Renyi and Tsallis entropy can be used for identification of optimal number in large textual collections. We also report results of numerical experiments of Semantic stability for 4 topic mode…
The paper studies practical estimation and interpretation of Rényi transfer entropy.
Paper proposes a Renyi entropy-based method for tuning hierarchical topic models.
The null energy condition is characterized via convexity of entropy in Lorentzian manifolds.
Feature selection, in the context of machine learning, is the process of separating the highly predictive feature from those that might be irrelevant or redundant. Information theory has been recognized as a useful concept for this task, as the prediction power stems from the correlation, i.e., the mutual information, …
The matrix-based Renyi's α-order entropy functional was recently introduced using the normalized eigenspectrum of a Hermitian matrix of the projected data in a reproducing kernel Hilbert space (RKHS). However, the current theory in the matrix-based Renyi's α-order entropy functional only defines the entropy of a single…
Novel kernelized Renyi's entropy improves deep learning generalization bounds.
Rényi divergence is related to Rényi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its or…
The paper solves portfolio selection using Rényi divergence and optimization.
Efficient approximations reduce computation of matrix-based Renyi's entropy.
This paper optimizes matrix-based Renyi's entropy computation for large datasets.
New bound limits generalization gap for large models, independent of model complexity.
In this paper, we quantify the statistical coherence between financial time series by means of the Renyi entropy. With the help of Campbell's coding theorem we show that the Renyi entropy selectively emphasizes only certain sectors of the underlying empirical distribution while strongly suppressing others. This accentu…
A new method for VAEs improves latent space disentanglement without violating probability laws.
Maximizes Rényi entropy for efficient exploration in reward-free RL.
Proposes an active RBI framework using Rényi information measures for more informed decision-making.
We prove the concavity of -Rényi entropy power for positive solutions to the doubly nonlinear diffusion equations on or compact Riemannian manifolds with nonnegative Ricci curvature. As applications, we give new proofs of the sharp -Sobolev inequality and -Gagliardo-Nirenberg inequalities on…
Paper introduces RCaI, a risk-sensitive control method using Rényi divergence.
Study introduces new curvature conditions for Lorentzian spaces using Rényi entropy.
We study the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. The minimum entropy required for such a latent is known as common entropy in information theory. We extend this notion to Renyi common entropy by minimizing the Renyi entropy of the …
We prove local Poincaré inequalities under various curvature-dimension conditions which are stable under the measured Gromov-Hausdorff convergence. The first class of spaces we consider is that of weak CD(K,N) spaces as defined by Lott and Villani. The second class of spaces we study consists of spaces where we have a …
With the help of transfer entropy, we analyze information flows between communities of complex networks. We show that the transfer entropy provides a coherent description of interactions between communities, including non-linear interactions. To put some flesh on the bare bones, we analyze transfer entropies between co…
The paper analyzes ESS metrics and their connections to entropy families.
The paper characterizes curvature-dimension conditions and related inequalities on Riemannian manifolds.
We propose a new policy iteration theory as an important extension of soft policy iteration and Soft Actor-Critic (SAC), one of the most efficient model free algorithms for deep reinforcement learning. Supported by the new theory, arbitrary entropy measures that generalize Shannon entropy, such as Tsallis entropy and R…
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A new family of multi-distribution divergences is characterized for fairness and other problems.
We present simple and computationally efficient nonparametric estimators of Rényi entropy and mutual information based on an i.i.d. sample drawn from an unknown, absolutely continuous distribution over . The estimators are calculated as the sum of -th powers of the Euclidean lengths of the edges of the `genera…
Unsupervised domain adaptation (UDA) aims at inferring class labels for unlabeled target domain given a related labeled source dataset. Intuitively, a model trained on source domain normally produces higher uncertainties for unseen data. In this work, we build on this assumption and propose to adapt from source to targ…
The paper improves semi-supervised learning using -divergences and -Rényi divergences.
Introduces TSI, a variance-based measure for persistence barcodes.
In this paper we consider the space of those probability distributions which maximize the -Rényi entropy. These distributions have the same parameter space for every , and in the case these are the normal distributions. Some methods to endow this parameter space with Riemannian metric is presented: the seco…
The entropy models have been recently adopted in many studies to evaluate the distribution of the shear stress in circular channels. However, the uncertainty in their predictions and their reliability remains an open question. We present a novel method to evaluate the uncertainty of four popular entropy models, includi…
In the framework of Multifractal Diffusion Entropy Analysis we propose a method for choosing an optimal bin-width in histograms generated from underlying probability distributions of interest. The method presented uses techniques of Rényi's entropy and the mean squared error analysis to discuss the conditions under whi…
New GAN loss functions improve image generation quality and stability.
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…
A new approach to -consistent estimation of a general density functional using -nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function of the densities at each point. The estimator is designed to be asymptotically unbiased, using t…
Generative models' evaluation scores can be misleading, leading to inflated grades.
Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynam…
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…
SMOTE is one of the oversampling techniques for balancing the datasets and it is considered as a pre-processing step in learning algorithms. In this paper, four new enhanced SMOTE are proposed that include an improved version of KNN in which the attribute weights are defined by mutual information firstly and then they …
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…
Paper extends information theory for efficient probabilistic modeling.
New framework controls generalization for heavy-tailed data in RLHF and SGLD.
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 …