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Estimating Entropy of Distributions in Constant Space
[article]

2019
*
arXiv
*
pre-print

We consider the task

arXiv:1911.07976v1
fatcat:yom3mxqtsbgo7dwudqdwxqohha
*of**estimating*the*entropy**of*k-ary*distributions*from samples*in*the streaming model, where*space*is limited. ... Our main contribution is an algorithm that requires O(k log (1/ε)^2/ε^3) samples and a*constant*O(1) memory words*of**space*and outputs a ±ε*estimate**of*H(p). ... We initiate the study*of**distribution**entropy**estimation*with*space*limitations, with the goal*of*understanding the*space*-sample trade-offs. ...##
###
Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples
[article]

2021
*
arXiv
*
pre-print

We develop a simple Quantile

arXiv:2102.12675v1
fatcat:kztvvxdqorhctolpzzt3kfl4ke
*Spacing*(QS) method for accurate probabilistic*estimation**of*one-dimensional*entropy*from equiprobable random samples, and compare it with the popular Bin-Counting (BC) method ... Bootstrapping is used to approximate the sampling variability*distribution**of*the resulting*entropy**estimate*, and is shown to accurately reflect the true uncertainty. ... The QS and BC algorithms used*in*this work are freely accessible for non-commercial use at https://github.com/rehsani/*Entropy*accessed on 20 February 2021. ...##
###
A Stochastic Non-Homogeneous Constant Elasticity of Substitution Production Function as an Inverse Problem: A Non-Extensive Entropy Estimation Approach

2013
*
Acta Physica Polonica. A
*

To apply the approach, we select a stochastic non-homogeneous

doi:10.12693/aphyspola.123.502
fatcat:p2sndzicgbhs3ojgb325zn5a2y
*constant*elasticity*of*substitution aggregated production function*of*the 27 EU countries which we*estimate*maximizing a non-extensive*entropy*... The document proposes a new*entropy*-based approach for*estimating*the parameters*of*nonlinear and complex models, i.e. those whose no transformation renders linear*in*parameters. ... (2) τ e*constant*elasticity*of*substitution, ε t stands for the random disturbance with unknown*distribution*. ...##
###
Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples

2021
*
Entropy
*

We develop a simple Quantile

doi:10.3390/e23060740
pmid:34208344
pmcid:PMC8231182
fatcat:tyaulcs5nzfadfymdj54c4sphu
*Spacing*(QS) method for accurate probabilistic*estimation**of*one-dimensional*entropy*from equiprobable random samples, and compare it with the popular Bin-Counting (BC) and ... Bootstrapping is used to approximate the sampling variability*distribution**of*the resulting*entropy**estimate*, and is shown to accurately reflect the true uncertainty. ... The QS and BC algorithms used*in*this work are freely accessible for non-commercial use at https://github.com/rehsani/*Entropy*accessed on 20 February 2021. ...##
###
Non-Extensive Entropy Econometrics: New Statistical Features of Constant Elasticity of Substitution-Related Models

2014
*
Entropy
*

We

doi:10.3390/e16052713
fatcat:hy5hvpuy5rctpo5smnzz2lzaci
*estimated*three stochastically distinct models*of**constant*elasticity*of*substitution (CES) class functions as non-linear inverse problem and showed that these PL related functions should have a closed ... The approach leads to robust*estimation*and to new findings about the true stochastic nature*of*this class*of*nonlinear-up until now-analytically intractable functions. ... Acknowledgments The author gratefully acknowledges University*of*Information Technology and Management*in*Rzeszow (Poland) for having financed this research. ...##
###
Optimal Partitions for Nonparametric Multivariate Entropy Estimation
[article]

2021
*
arXiv
*
pre-print

Such optimal partitions were observed to be more accurate than existing techniques

arXiv:2112.06299v1
fatcat:35dyo3snuvhwlakyk5ljx3v4sa
*in**estimating**entropies**of*correlated bivariate Gaussian*distributions*with known theoretical values, across varying sample ... This paper demonstrates that the application*of*rotation operations can improve*entropy**estimates*by aligning the geometry*of*the partition to the sample*distribution*. ... ., x N }, the uncertainty*of*the*distribution*can be*estimated*from the partitioned sample*space*, by calculating the*entropy**of*the probability density*estimator*using a histogram approach. ...##
###
Streaming and sublinear approximation of entropy and information distances

2006
*
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
*

*In*a data stream setting (sublinear

*space*), we give the first algorithm for

*estimating*the

*entropy*

*of*a

*distribution*. ... Our algorithm runs

*in*polylogarithmic

*space*and yields an asymptotic

*constant*factor approximation scheme. ... We consider the problem

*of*

*estimating*the

*entropy*H

*of*a

*distribution*, providing optimal (up to

*constants*) upper bounds for testing

*entropy*. ...

##
###
Projective Power Entropy and Maximum Tsallis Entropy Distributions

2011
*
Entropy
*

A close relation

doi:10.3390/e13101746
fatcat:e24fizjbm5b4ffb3dcazafziwe
*of*the*entropy*with the Lebesgue*space*L p and the dual L q is explored,*in*which the escort*distribution*associates with an interesting property. ... We discuss the statistical*estimation*by minimization*of*the empirical loss associated with the projective power*entropy*. ... Model*of*Maximum*Entropy**Distributions*We will elucidate a dualistic structure between the maximum*entropy*model on H γ , defined*in*(2) and the minimum cross*entropy**estimator*on C γ , defined*in*(1) ...##
###
Streaming and Sublinear Approximation of Entropy and Information Distances
[article]

2005
*
arXiv
*
pre-print

*In*a stream setting (sublinear

*space*), we give the first algorithm for

*estimating*the

*entropy*

*of*a

*distribution*. ... Efficient

*estimation*

*of*these distances is a key component

*in*algorithms for manipulating

*distributions*. ... We consider the problem

*of*

*estimating*the

*entropy*H

*of*a

*distribution*, providing optimal (upto

*constants*) upper bounds for testing

*entropy*. ...

##
###
A frequency-domain entropy-based detector for robust spectrum sensing in cognitive radio networks

2010
*
IEEE Communications Letters
*

The

doi:10.1109/lcomm.2010.06.091954
fatcat:zu6vhpobnve6xfkyl74luqnhee
*entropy**of*the sensed signal is*estimated**in*the frequency domain with a probability*space*partitioned into fixed dimensions. ... To counteract noise uncertainty, a new*entropy*-based spectrum sensing scheme is introduced*in*this letter. ... The*entropy**of*the measured signal is*estimated**in*the frequency domain with the probability*space*partitioned into fixed dimensions. ...##
###
Association Rule Mining using Maximum Entropy
[article]

2015
*
arXiv
*
pre-print

We consider the use

arXiv:1501.02143v1
fatcat:zfbnapgaffdwhahhmd2jgwqnlq
*of*maximum*entropy*probability*estimates*, which give a principled way*of*extrapolating probabilities*of*events that do not even occur*in*the data set! ...*entropy**estimates*, and 2) Maximum*entropy**estimates*based on a small number*of*samples are provably tightly concentrated around the true maximum*entropy*frequency that arises if we let the number*of*samples ... We note that a similar proof*of*how to find the maxent*estimate*appears*in*[8] , however we give explicit*constants**in*Equation (14) whereas their proof shows existence*of*the*constants*. ...##
###
Estimation of entropy measures for categorical variables with spatial correlation
[article]

2019
*
arXiv
*
pre-print

*Entropy*is a measure

*of*heterogeneity widely used

*in*applied sciences, often when data are collected over

*space*. ... We propose a path for spatial

*entropy*

*estimation*: instead

*of*correcting the global

*entropy*

*estimator*, we focus on improving the

*estimation*

*of*its components, i.e. the probabilities,

*in*order to account ...

*In*the case

*of*categorical variables following, e.g., a multinomial

*distribution*, the crucial point is to

*estimate*the

*distribution*parameters. ...

##
###
Geodesic Entropic Graphs for Dimension and Entropy Estimation in Manifold Learning

2004
*
IEEE Transactions on Signal Processing
*

*In*this paper, we consider the closely related problem

*of*

*estimating*the manifold's intrinsic dimension and the intrinsic

*entropy*

*of*the sample points. ...

*In*the manifold learning problem, one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded

*in*a higher dimensional linear vector

*space*, based on a set

*of*measured sample points ... Almal for their help

*in*acquiring and processing these face images. ...

##
###
Detecting temperature fluctuations at equilibrium
[article]

2015
*
arXiv
*
pre-print

Numerical evidence using an analytically tractable model shows that the effects

arXiv:1503.01808v1
fatcat:2oqq7so6v5afloe5fiavcp7nim
*of*temperature fluctuations can be detected*in*equilibrium and dynamical properties*of*the phase*space**of*the small system ... We interpret this ambiguity as resulting from a stochastically fluctuating temperature coupled with the phase*space*variables giving rise to a broad temperature*distribution*. ... Acknowledgment: We thank Ken Dill, Steve Pressé, Dilip Asthagiri for a critical reading*of*the manuscript. ...##
###
5 Estimating the CGE Model through the Maximum Entropy Principle
[chapter]

2019
*
Non-Extensive Entropy Econometrics for Low Frequency Series
*

*In*their reference work, Arndt et al. (2002) present a new approach to

*estimating*parameters

*of*a CGE model through maximum

*entropy*. That approach is pursued here. ... Whatever class

*of*CGE model is

*in*use, it displays consistent drawbacks, such as the lack

*of*efficient methodology for the

*estimates*

*of*behavioural parameters (e.g., trade parameters), less realistic economic ... Application: Non-Extensive

*Entropy*and

*Constant*Elasticity

*of*Substitution-Based Models The example below shows the possibility

*of*carrying out robust

*estimation*

*of*a stochastic

*constant*elasticity

*of*...

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