Asymptotic Efficiency of Maximum Entropy Estimates

Doklady Mathematics - The problem of entropy estimation of probability density functions with allowance for real data is posed (the maximum entropy estimation (MEE) problem). Global existence...     

区间概率信息条件下的风险型决策问题的解法探讨

区间概率信息条件下的决策问题是介于不确定型决策与风险型决策之间的一类特殊的决策问题。基于区间概率的定义及其数学特征,利用最大熵准则将区间概率转化为点概率,从而实现了区间概率信息条件决策问题的求解。     

基于最大熵原理的测量不确定度商概率建模及计算

测量数学模型建立后,测量不确定度评定需考虑输入量的不确定度及分布的传递性.若测量模型为幂指数积模型,通常先将输入量线性化,再采用合成方差的方法计算被测量的不确定度,方法计算简便,但未揭示不确定度随分布传递这一现象.针对问题,首先运用最大熵原理,计算测量仪器分辨力已知时,输入量的概率密度函数,其结果显示输入量服从矩形分布;其次重点推导了输入量与被测量之间为商概率模型时,被测量的概率密度函数、估计值和测量不确定度,并给出不确定度评定的具体步骤;最后利用恒流源测量高精密小电阻实例的对比分析,说明了该不确定度评定模型的可行性和有效性.     

期权定价的最大熵方法

以欧式期权为例,用标的资产(如股票风险资产)和无风险资产复制期权,并用自融资无套利原理分析金融市场的资产价值变化情况.在此基础上,通过最大熵原理来求得资产组合中每个资产所占的比重,进而得出期权定价模型,由于最大熵原理所求得概率分布是目前所知求概率分布方法中最客观、无偏的,所以求得的新模型不受金融市场类型和标的资产价格分布的限制,具有较强的客观、无偏、可预测性.通过对期权的常用算例计算,发现新模型比B-S模型以及一些其它熵期权定价模型有更准确的标的资产价格分布、更低的回溯测试误差.     

Restoration of Degraded Images with Maximum Entropy

We present a Maximum Entropy based approach to the restoration ofdegraded images as an alternative to restorationtechniques using inverse Wiener filtering.The method we discuss applies in particularto images corrupted by a relativelyhigh system noise. A variety of experimental results supportingour imaging model are included.     

估计死亡率分布的一个最大熵模型

本文提出了一种估计死亡率分布的新模型一最大熵模型。该模型直接从样本信息出发，不需要对待估分布的概率密度函数或先验分布作任何假定，从而克服了极大似然估计和贝叶斯估计的不足。而且通过两个例子的计算结果，表明该方法与样本数据的拟合效果要好于其它两种方法。     

Logistic回归系数极大似然估计的计算

本文介绍了Logstic回归系数的极大似然估计（maximum likelihood）的计算,并引入Levenberg—Marquardt算法,通过这代给出了Logistic回归系数的极大似然估计。     

推理规则的信息熵描述

根据信息理论的一些基本观点首次定义了决策逻辑系统中公式的信息熵,由此给出了知识系统中推理规则信息熵的定义。然后讨论了推理规则信息熵的某些性质。随后又建立了一些推理规则信息熵有关的若干重要概念,从而揭示了信息论与知识表达系统之间的某些联系,为信息理论应用于人工智能及数据挖掘提供了一定的理论或技术性工具。     

Geometric Inference for Probability Measures

Data often comes in the form of a point cloud sampled from an unknown compact subset of Euclidean space. The general goal of geometric inference is then to recover geometric and topological features (e.g., Betti numbers, normals) of this subset from the approximating point cloud data. It appears that the study of distance functions allows one to address many of these questions successfully. However, one of the main limitations of this framework is that it does not cope well with outliers or with background noise. In this paper, we show how to extend the framework of distance functions to overcome this problem. Replacing compact subsets by measures, we introduce a notion of distance function to a probability distribution in ℝ ^d . These functions share many properties with classical distance functions, which make them suitable for inference purposes. In particular, by considering appropriate level sets of these distance functions, we show that it is possible to reconstruct offsets of sampled shapes with topological guarantees even in the presence of outliers. Moreover, in settings where empirical measures are considered, these functions can be easily evaluated, making them of particular practical interest.     

非线性l_1问题的极大熵方法

本文给出求解非线性l1问题的极大熵方法．介绍了极大熵函数的性质,极大熵算法及其收敛性,最后给出一个算例。     

非线性l1问题的极大熵方法

本文给出求解非线性l1问题的极大熵方法,介绍了极大熵函数的性质,极大熵算法及其收敛性。最后给出一个算例。     

Asymptotic Estimates of Elementary Probability Distributions

Several new asymptotic estimates (with precise error bounds) are derived for Poisson and binomial distributions as the parameters tend to infinity. The analytic methods used are also applicable to other discrete distribution functions.     

Maximum Norm Resolvent Estimates for Elliptic Finite Element Operators

We study a finite element approximation A _h, based on simplicial Lagrange elements, of a second order elliptic operator A under homogeneous Dirichlet boundary conditions in two and three dimensions, where h is thought of as a meshsize. The main result of the paper is a new resolvent estimate for the operator A _h in the L -norm. This estimate is uniform with respect to h for the case with at least quadratic elements. In the case with linear elements, the estimate contains on the right a factor proportional to (log log ), where = 1 or = in two or three dimensions, respectively.This revised version was published online in October 2005 with corrections to the Cover Date.     

截尾线性回归模型参数极大似然估计的存在性和唯一性

考虑带有截尾数据的线性回归模型,在较为-般的截尾数据情形下,本文给出了其参数极大似然估计(MLE)存在且唯一的充分必要条件,且对MLE不存在的样本数据集Q的描述定义更为准确.     

Maximum Conditional Probability Stochastic Controller for Linear Systems with Additive Cauchy Noises

Journal of Optimization Theory and Applications - Motivated by the sliding mode control approach, a stochastic controller design methodology is developed for discrete-time, vector-state linear...     

Maximum Entropy Condition in Queueing Theory

The main results in queueing theory are obtained when the queueing system is in a steady-state condition and if the requirements of a birth-and-death stochastic process are satisfied. The aim of this paper is to obtain a probabilistic model when the queueing system is in a maximum entropy condition. For applying the entropic approach, the only information required is represented by mean values (mean arrival rates, mean service rates, the mean number of customers in the system). For some one-server queueing systems, when the expected number of customers is given, the maximum entropy condition gives the same probability distribution of the possible states of the system as the birth-and-death process applied to an M/M/1 system in a steady-state condition. For other queueing systems, as M/G/1 for instance, the entropic approach gives a simple probability distribution of possible states, while no close expression for such a probability distribution is known in the general framework of a birth-and-death process.