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maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support

JOURNAL OF COMPUTATIONAL PHYSICS 2009年第24期228卷 9079-9091页

作者： Gotovac, Hrvoje Gotovac, Blaz Univ Split Dept Civil & Architectural Engn Split 21000 Croatia KTH Dept Land & Water Resources Engn S-10044 Stockholm Sweden

The maximum entropy (MaxEnt) principle is a versatile tool for statistical inference of the probability density function (pdf) from its moments as a least-biased estimation among all other possible pdfs. It maximizes Shannon entropy, satisfying the moment constraints. Thus, the MaxEnt algorithm transforms the original constrained optimization problem to the unconstrained dual optimization problem using Lagrangian multipliers. The Classic Moment Problem (CMP) uses algebraic power moments, causing typical conventional numerical methods to fail for higher-order moments (m > 5-10) due to different sensitivities of Lagrangian multipliers and unbalanced nonlinearities. Classic MaxEnt algorithms overcome these difficulties by using orthogonal polynomials, which enable roughly the same sensitivity for all Lagrangian multipliers. In this paper, we employ an idea based on different principles, using Fup(n) basis functions with compact support, which can exactly describe algebraic polynomials, but only if the Fup order-n is greater than or equal to the polynomial's order. Our algorithm solves the CMP with respect to the moments of only low order Fup(2) basis functions, finding a Fup(2) optimal pdf with better balanced Lagrangian multipliers. The algorithm is numerically very efficient due to localized properties of Fup(2) basis functions implying a weaker dependence between Lagrangian multipliers and faster convergence. Only consequences are an iterative scheme of the algorithm where power moments are a sum of Fup(2) and residual moments and an inexact entropy upper bound. However, due to small residual moments, the algorithm converges very quickly as demonstrated on two continuous pdf examples - the beta distribution and a bi-modal pdf, and two discontinuous pdf examples - the step and double Dirac pdf. Finally, these pdf examples present that Fup MaxEnt algorithm yields smaller entropy value than classic MaxEnt algorithm, but differences are very small for all practical engi

关键词： maximum entropy algorithm Classic Moment Problem Fup basis functions Compact support

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maximum-entropy algorithm APPLIED TO IMAGE-ENHANCEMENT

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IEE PROCEEDINGS-E COMPUTERS AND DIGITAL TECHNIQUES 1980年第5期127卷 170-172页

作者： DANIELL, GJ GULL, SF UNIV CAMBRIDGE CAVENDISH LABMULLARD RADIO ASTRON OBSERVCAMBRIDGE CB3 0HEENGLAND

A model is suggested for assigning the prior probability of an image in Bayes' theorem which leads to a very general algorithm for image enhancement. Examples of sharpening blurred photographs show how the success... 详细信息

关键词： Bayes' theorem deconvolution maximum entropy algorithm Optical information, image and video signal processing Pattern recognition image enhancement picture processing

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Optimizing the transformation of HYSCORE data using the maximum entropy algorithm

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JOURNAL OF MAGNETIC RESONANCE 2019年 301卷 30-39页

作者： Motygullina, Alina E. Mobli, Mehdi Harmer, Jeffrey R. Univ Queensland Ctr Adv Imaging St Lucia Qld 4072 Australia

Non-uniform sampling (NUS) in combination with the maximum entropy (MaxEnt) algorithm as applied to multi-dimensional NMR data has been thoroughly investigated and the NUS approach shown to provide significant sensitivity improvements as compared to methods using uniformly sampled (US) data and the discrete Fourier transform (DFT). Hyperfine sublevel correlation (HYSCORE) is a standard pulse EPR experiment that can potentially benefit greatly from this approach, but the data present unique challenges as compared to NMR. HYSCORE data typically exhibit a very large range of peak intensities, signals are in the form of irregularly shaped ridges with variable intensities, and time traces are generally truncated to save measurement time. MaxEnt has the advantageous properties that it does not require US data, dampens weak signals (noise) and does not suffer from windowing artifacts due to truncation of the time traces. Critical to the success of the MaxEnt algorithm is the choice of the two input parameters aim and def which describe the data noise and contribution of entropy in the optimization, respectively. In this paper we expand our preliminary study on the application of MaxEnt to the reconstruction of HYSCORE spectra to include a detailed analysis on sensitivity to detect weak peaks, investigate the non-linearity of the transformation and ascertain if it can be characterized by the introduction of synthetic peaks, and define a general range for the choice of aim and def. Furthermore, the ability of the MaxEnt method to remove windowing artefacts in uniformly sampled truncated HYSCORE data is described. (C) 2019 Published by Elsevier Inc.

关键词： EPR HYSCORE Non-uniform sampling maximum entropy algorithm

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Numerical simulation analysis of ecological monitoring of small reservoir dam based on maximum entropy algorithm

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OPEN GEOSCIENCES 2023年第1期15卷

作者： Wang, Qing Zhou, Zhiwei Tang, Shaolong Wan, Siyuan Yu, Weiran Jiangxi Acad Water Sci & Engn Nanchang 330029 Jiangxi Peoples R China Jiangxi Prov Hydraul Safety Engn Technol Res Ctr Nanchang 330029 Jiangxi Peoples R China

Displacement monitoring method of reservoir dam is a key research topic at present. In order to better display the overall efficiency of horizontal displacement and vertical displacement monitoring, a numerical simulation analysis method of ecological monitoring of small reservoir dam based on the maximum entropy algorithm is proposed. The virtual value is calculated by the maximum entropy algorithm, and the probability distribution function of random variables is obtained. The comprehensive prediction model of ecological monitoring results is constructed by the probability distribution function, and the daily monitoring values of ecological history of small reservoir dams are obtained. The maximum entropy probability density function is used to calculate the initial moment of small reservoir displacement samples, calculate the abnormal probability of the dam, get the maximum entropy probability density, realize the unbiased distribution of simulation values, and complete the dam deformation monitoring of small reservoirs. The simulation experiment is verified by numerical simulation. The results show that this method can effectively monitor the horizontal and vertical displacement of the dam;monitor the water-level hydrograph of pressure pipes at each measuring point;and obtain the changes of ecological runoff, temperature difference, and sediment discharge around the dam of small reservoirs in real time, which provides data guarantee for improving the ecological added value of small reservoirs.

关键词： maximum entropy algorithm small reservoir dam ecological monitoring pressure tube water level probability distribution function the vertical displacement

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maximum entropy algorithm of multi-objective smoothless semi-infinite programming and its convergence

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Huazhong Ligong Daxue Xuebao/Journal Huazhong (Central China) University of Science and Technology 2001年第1期29卷 85-86页

作者： Cen, L. Shi, B. Dept. of Mathematics HUST Wuhan 430074 China

maximum entropy algorithm for approximating multi-objective smoothless semi-infinite programming is presented. The convergence of the approximating algorithm is obtained in general from the convergence of the series o... 详细信息

关键词： Convergence maximum entropy algorithm Multi-objective programming Semi-infinite programming

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Research on the Application of maximum entropy Based algorithm in Precipitation Forecasting 24

Research on the Application of Maximum Entropy Based Algorit...

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4th International Conference on Internet of Things and Machine Learning

作者： Tian, Huaiying Zhou, Xiaoguang Zhou, Ming Army 91206 Qingdao Peoples R China Army 91475 Qingdao Peoples R China Team 18 Army 92919 Qingdao Peoples R China

ISBN: (纸本)9798400710353

Precipitation forecasting is crucial in meteorology as well as in fields such as agriculture and urban planning. This paper investigates the application of the maximum entropy algorithm in precipitation forecasting, exploring its unique advantages in handling complex meteorological data. By comparing it with traditional BP neural network algorithms, the paper provides a detailed analysis of the maximum entropy algorithm's performance in data processing, model training, and prediction accuracy. The results indicate that the maximum entropy algorithm offers superior precision and stability in precipitation forecasting, effectively addressing data diversity and uncertainty. These advantages position it as a promising method for precipitation prediction, contributing to enhanced accuracy and reliability in meteorological forecasts and providing scientific basis and technical support for related fields.

关键词： maximum entropy algorithm Neural networks Precipitation forecasting Applied research

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Ecosystem service trade-offs weaken ecological network interactions

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JOURNAL OF CLEANER PRODUCTION 2025年 508卷

作者： Xie, Jing Xie, Binggeng Li, Junhan Zhang, Xuemao Pang, Xiaofei Hunan Normal Univ Sch Geog Sci Changsha 410081 Peoples R China Chinese Acad Sci Inst Geochem State Key Lab Environm Geochem Guiyang 550081 Peoples R China

Clarifying the relationship between ecological networks and ecosystem services will help to enhance regional biodiversity and human well-being. This study evaluated bird suitability in Changsha-Zhuzhou-Xiangtan urban agglomeration through field observations and maximum entropy model, and combined with distance thresholds to identify ecological networks. Network weights were quantified by an improved gravity model. The trade-off and synergistic between ecosystem services were determined, and we examined the relationship between bird ecological networks and ecosystem services from two perspectives: "substituting 'time' by 'space'" and "period differences", respectively. Following are the key findings: Average AUC of the ten iterations of MaxEnt model reached 0.8226, and the threshold of bird dispersal distance was 2300-3000 m. Bird ecological network underwent source degradation and corridor breakup during 2000-2020, in which the highest value of source area declined from 3701 km2 to 3400 km2. Counties at the edge had greater interaction forces, with the highest value of 114130.26, and had spatial spillovers. Trade-off strength of SC and HQ decreased from 0.593 to 0.569 in Yuanjiang and from 0.803 to 0.782 in Yueyang County, accompanied by an increase in the network force between the two counties from 22969.14 to 40026.65. Thus, decreases in the strength of trade-offs had positive effects on ecological network, while changes in the relationships from synergistic to trade-offs weakened interaction forces. Future urban planning should focus on monitoring the dynamics of bird network interactions at county boundaries, attending to stepping stone within buffer zones, and factoring in ecosystem service enhancement priorities and trade-off reduction.

关键词： Ecological network Ecosystem service Trade-offs maximum entropy algorithm Interaction force

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maximum entropy decoding of multivariate neural spike trains

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BMC Neuroscience 2009年第1期10卷 1-2页

作者： Hélène Seiler Yang Zhang Aman B Saleem Phil Bream John Apergis-Schoute Simon R Schultz Department of Physics Imperial College London London SW7 2AZ UK Department of Bioengineering Imperial College London London SW7 2AZ UK

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A note on a minimax rule for portfolio selection and equilibrium price system

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APPLIED MATHEMATICS AND COMPUTATION 2009年第1期208卷 49-57页

作者： Wu, Zhu-Wu Song, Xue-Feng Xu, Ying-Ying Liu, Kun China Univ Min & Technol Sch Sci Xuzhou 221116 Peoples R China China Univ Min & Technol Sch Management Xuzhou 221116 Peoples R China

This paper concerns a minimax model to investigate the optimal portfolio selection problem without riskless assets and with or without short sale restriction. A numerical solution to the problem with short sale restriction is obtained by using the maximum entropy algorithm. For the problem without short sale restriction, we derive a analytical expression for the optimal solution, a sufficient condition for the existence and uniqueness of a nonnegative equilibrium price system, and an explicit formula for the price system. Furthermore, a numerical example is given to show the validity of the method. (C) 2008 Elsevier Inc. All rights reserved.

关键词： Portfolio selection Minimax model Optimization Efficient frontier maximum entropy algorithm

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Quantifying bursting neuron activity from calcium signals using blind deconvolution

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JOURNAL OF NEUROSCIENCE METHODS 2013年第2期218卷 196-205页

作者： Park, In Jun Bobkov, Yuriy V. Ache, Barry W. Principe, Jose C. Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA Univ Florida Ctr Smell & Taste Whitney Lab Gainesville FL 32611 USA Univ Florida McKnight Brain Inst Gainesville FL 32611 USA Univ Florida Dept Biol Gainesville FL 32611 USA Univ Florida Dept Neurosci Gainesville FL 32611 USA

Advances in calcium imaging have enabled studies of the dynamic activity of both individual neurons and neuronal assemblies. However, challenges, such as unknown nonlinearities in the spike-calcium relationship, noise, and the often relatively low temporal resolution of the calcium signal compared to the time-scale of spike generation, restrict the accurate estimation of action potentials from the calcium signal. Complex neuronal discharge, such as the activity demonstrated by bursting and rhythmically active neurons, represents an even greater challenge for reconstructing spike trains based on calcium signals. We propose a method using blind calcium signal deconvolution based on an information-theoretic approach. This model is meant to maximise the output entropy of a nonlinear filter where the nonlinearity is defined by the cumulative distribution function of the spike signal. We tested our maximum entropy (ME) algorithm using bursting olfactory receptor neurons (bORNs) of the lobster olfactory organ. The advantage of the ME algorithm is that the filter can be trained online based only on the statistics of the spike signal, without any assumptions regarding the unknown transfer function characterizing the relation between the spike and calcium signal. We show that the ME method is able to more accurately reconstruct the timing of the first and last spikes of a burst compared to other methods and that it improves the temporal precision fivefold compared to direct timing resolution of calcium signal. (c) 2013 Elsevier B.V. All rights reserved.

关键词： Calcium imaging Olfactory receptor neuron Blind deconvolution Information-theoretic approach maximum entropy algorithm

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