The philosophy of maximum entropy me estimation can be stated in two principles. Maximum entropy estimation of density and regression functions. When only a frequency table is used in the estimation, we can directly compare the twoknown, asymptotically efficient estimators, mle and gmm 2, to gmm s. We derive two more general estimation methods by replacing the gmes entropy objective with higherorder entropy indexes. Unlike most other work on the estimation of complete information games, the method we proposed is data constrained and does not. A generalized maximum entropy gme estimation approach to. Conditional maximum entropy me models provide a general purpose machine learning technique which has been successfully applied to fields as diverse as computer vision and econometrics, and which is used for a wide variety.
Journal of the american statistical association, 74 1979, pp. The maximum entropy maxent approach to probability distribution estimation was. Maximum entropy estimation of probability distribution of. Inequality restricted maximum entropy estimation in stata. Correcting sample selection bias in maximum entropy. Similar to support vector machine estimators, the maximum entropy principle may require the solution to a quadratic programming and thus provide a sparse mixture model as the optimal density estimator. Maximum entropy spectral estimation is a method of spectral density estimation. Kelley pace bayesian model choice in spatial econometrics leslie w. A comparison of algorithms for maximum entropy parameter. The maximum entropy principle can be used to assign utility values when only partial information is available about the decision makers preferences.
Hx takes the equation of a statistical mechanics property known as entropy, which. In the theory and practice of econometrics the model, the methodand the data are all interdependent links in informationrecovery estimation and inference. If the constraints cannot be satisifed for any values of s, then the maximum entropy distribution does not exist. Entropy is a concept that originated in thermodynamics, and later, via statistical mechanics, motivated entire branches of information theory, statistics, and machine learning maximum entropy is the state of a physical system at greatest disorder or a statistical model of least encoded information, these being important theoretical analogs maximum entropy may refer to. Maximum entropy estimation of continuous distribution series on econometrics and management sciences on free shipping on qualified orders. The approach we take in establishing the asymptotic properties concomitantly identifies a new. Rats is used worldwide by economists and others for analyzing time series and cross sectional data, developing and estimating econometric models, forecasting, and much more.
An introduction to maximum entropy and minimum crossentropy estimation using stata article in stata journal 103. Carter hillz inequality restricted maximum entropy estimation in stata 1. Aug 18, 2005 here is an incomplete list of software found on the net that are related to maximum entropy modeling. Generalized maximum entropy estimation of discrete sequential. Wadsworth advanced books and software, wadsworth and brookscole, pacific grove, ca 1985. Entropy balancing thereby exactly adjusts inequalities in representation with respect to the first, second, and possibly higher moments of the covariate distributions.
Gmm estimation of a maximum entropy distribution with. Maxentmodels and discriminative estimation generative vs. Maximum entropy and minimum crossentropy estimation are applicable when faced with illposed estimation problems. Disciplines other computer sciences comments university of pennsylvania institute for research in cognitive science technical report no.
In this article, we describe the gmentropylogit command, which implements the generalized maximum entropy estimation methodology for discrete choice models. An introduction to entropy estimation of parameters in. The measures are based on the concepts of differential entropy and fisher information and describe the spread or variability of the random variable from a different point of view than the ubiquitously used concept of. These are the contents of our online econometrics textbook. Maximum entropy estimation in economic models with linear. Statistics, econometrics and forecasting by arnold zellner.
A comparison of algorithms for maximum entropy parameter estimation. Maximum entropy distributions and exponential family where the f gs are chosen such that f x satis es the constraints. Maximum entropy estimation of chinese household expenditure survey data. Modeling multisite streamflow dependence with maximum.
This is the exponential distribution with density f. Maximum entropy econometrics will be of interest to econometricianstrying to devise procedures for recovering information from partialor incomplete data, as well as quantitative economists in financeand business, statisticians, and students and applied researchersin econometrics, engineering and the physical sciences. Spatial and spatiotemporal econometrics ebook, 2004. Faced with these problems, maximum entropy economeirics provides a new basis for learning from economic and statistical models that may be nonregular in the sense that they are illposed or. Dissertation, department of agricultural economics, washington state university, august 2000.
The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge is the one with largest entropy, in the context of precisely stated prior data such as a proposition that expresses testable information. The results obtained by maximizing s in the previous section can be derived by minimizing a relative entropy re defined above with the discrete distributions, q and a uniform distribution, u, where the integral in equation 9 is replaced by a summation. In this paper, freight transportation is taken into account. Now we formally prove that f, as derived above, is indeed the maximum entropy distribution. Department of biophysics program, the ohio state university, columbus, oh. Maximum entropy is the state of a physical system at greatest disorder or a statistical model of least encoded information, these being important theoretical analogs. Marginal likelihood estimation with the crossentropy method.
The problem of binary classification is considered, an algorithm for its solution is proposed, based on the method of entropybased estimation of the decision rule parameters. Great java maxent implementation with gis training algorithm. In the theory and practice of econometrics the model, the methodand the data are all interdependent links in informationrecoveryestimation and inference. We propose a dataconstrained generalized maximum entropy gme estimator for discrete sequential move games of perfect information which can be easily implemented on optimization software with highlevel interfaces such as gams. The uniform distribution result is also very encouraging when estimating a. The maximum entropy variational principle for single channel power spectral analysis chapter 2 pdf 94 kb ps. The econometrics section contains chapters about econometrics see also free calculator, regression extensions, mathematical models, and boxjenkins time series analysis forecasting. Use of generalized maximum entropy estimation for freight. This information theoretic procedure is preferred over its maximum likelihood counterparts because it is more efficient, avoids strong parametric assumptions, works well when the sample. In order to obtain such utility values it is necessary to establish an analogy between probability and utility through the notion of a utility density function.
Bayesian methods and entropy in economics and econometrics. Inequality restricted maximum entropy estimation in stata randall campbelly, r. Matlab code for univariate maximum entropy density estimation for details, see calculation of maximum entropy densities with application to income distribution, journal of econometrics, 115 2003. A detailed description of the entropybased estimation method and the classification algorithm is given, the advantages and disadvantages of this approach are described, the results of. However, maximum entropy models fit to small data sets can be subject to sampling bias. Maximum entropy estimation of probability distribution of variables. Maximum likelihood and entropy thirdorderscientist. Maximum entropy distribution estimation with generalized. Robinson, s, cattaneo, a, and elsaid, m, updating and estimating a social accounting matrix using cross entropy methods. Another important application of information theory in econometrics is formalized as maximum entropy econometrics golan et al. Many distributions in statistics can be characterized as having maximum entropy. Entropy free fulltext estimation bias in maximum entropy. An introduction to maximum entropy and minimum cross.
The results obtained by maximizing s in the previous section can be derived by minimizing a relative entropy re defined above with the discrete distributions, q and a uniform distribution, u, where the integral in equation 9 is replaced by a. An adaptive empirical bayes estimator of the multivariate normal mean under quadratic loss, journal of econometrics, elsevier, vol. Journal of econometrics 8 2007 532546 gmm estimation of a maximum entropy distribution with interval data ximing wua, jeffrey m. In various scienceengineering applications, such as independent component analysis, image analysis, genetic analysis, speech recognition, manifold learning, evaluation of the status of biological systems and time delay estimation it is useful to estimate the differential entropy of a system or process, given some observations the simplest and most common approach uses. K 1990, orthogonal basis and maximum entropy estimation of probability density and regression functions, doctoral dissertation, department of economics, university of chicago. Seldom, however, are theeconomic and statistical models correctly specified, the datacomplete or capable of being replicated, the estimation rulesoptimal and the inferences free of distortion. Maximum entropy models have become popular statistical models in neuroscience and other areas in biology and can be useful tools for obtaining estimates of mutual information in biological systems. The dataconstrained generalized maximum entropy estimator. Carter hillz mississippi state universityy, louisiana state universityz stata conference new orleans july 18, 20 randall campbelly, r.
Here is an incomplete list of software found on the net that are related to maximum entropy modeling. Maximum entropy method for estimating the reproduction number. Nonparametricmaximumentropyprobabilitydensityestimation. In the first experiment, we generate the sample from the standard normal distribution and assume the functional form is known. Correcting sample selection bias in maximum entropy density estimation miroslav dudk, robert e. Foreign direct investment fdi becomes a pillar for economic development. Ryu ewha unicersitv, seoul, korea received december 1990. The estimation and testing of spatial econometric models are studied by whit tle 1954. Re always remains positive with a lower bound at zero. Estimation of entropy and mutual information 1195 ducing anything particularly novel, but merely formalizing what statisticians have been doing naturally since well before shannon wrote his papers. A common statistical situation concerns inferring an unknown distribution qx. Entropy econometrics developed by golan, judge and miller 1996 offers a useful approach for improving the assumptions made about parameters in economic models. Unlike most other work on the estimation of complete information games, the method we proposed is data constrained and.
One of the main applications of the maximum entropy principle is in discrete and continuous density estimation. Maximum likelihood and entropy cosma shalizi posted recently about optimization for learning. Maximum entropy econometrics will be of interest to econometricians trying to devise procedures for recovering information from partial or incomplete data, as well as quantitative economists in finance and business, statisticians, and students and applied researchers in econometrics, engineering and the physical sciences. The density of the atmosphere does indeed have this distribution. Maximum entropy estimation of probability distribution of variables in higher dimensions from lower dimensional data jayajit das14, sayak mukherjee1,2, and, susan e. This information theoretic procedure is preferred over its maximum likelihood counterparts because it is more efficient, avoids strong parametric assumptions, works well when the sample size is small, performs. The generalized maximum entropy gme estimation method golan, judge, and miller, 1996 has been widely used for linear and nonlinear estimation models. We then show that the gme is the only estimation technique that is. Entropybased estimation in classification problems.
I show how this command can be used to calibrate survey data to various population totals. Maximum entropy methods of parameter estimation are appealing because they impose no additional structure on the data, other than that explicitly assumed by the analyst. Empirical likelihood, entropy, estimating equations, and. Take precisely stated prior data or testable information about a probability distribution. I introduce a stata command that estimates a probability distribution using a maximum entropy or minimum crossentropy criterion. I introduce a stata command that estimates a probability distribution using a maximum entropy or minimum cross entropy criterion. Pdf maximum entropy method for estimating the reproduction. However, the flexibility of me models is not without cost. Entropy estimation, developed by golan, judge and miller 1996, is an approach that allows economic modellers to use data to improve the assumptions they make about parameters in economic models.
The dataconstrained generalized maximum entropy estimator of. Iii if the density has xed variance then the di erential entropy is maximized by the gaussian density. This strategy bears a striking resemblance to regularization methods employed in abstract statistical inference grenander, 1981, generally known. Estima develops and sells rats regression analysis of time series, a leading econometrics and timeseries analysis software package. These balance improvements can reduce model dependence for the subsequent estimation of treatment effects. Use of generalized maximum entropy estimation for freight flows. An introduction to maximum entropy and minimum crossentropy. As a starting point, it takes prior information whether from previous studies, theory, or educated guesses in the form of a probability distribution. Selected paper for the 2000 waea meetings, vancouver, canada.
Logistic regression, conditional loglinear or maximum pcd entropy models, conditional random fields also, svms, averaged perceptron, etc. Hepple a bayesian probit model with spatial dependencies tony e. Journal of data science 102012, 7586 use of generalized maximum entropy estimation for freight flows modelling and an application esra satici1 and haydar demirhan2 1general directorate of turkish highways and 2hacettepe university abstract. Northholland maximum entropy estimation of density and regression functions hang k. We address the problem of nonparametric estimation of the recently proposed measures of statistical dispersion of positive continuous random variables. Maximum entropy markov models and logistic regression.
Karpa maximum entropy approach to estimation and inference in dynamic models or counting fish in the sea using maximum entropy j. In this paper we prove that the data constrained gme estimator of the general linear model is consistent and asymptotically normal. The goal is to improve the spectral quality based on the principle of maximum entropy. Amis a maximum entropy estimator for feature forests. Given an entropy source with discrete random variable x with possible values. This study explores which association of southeast asian nations asean6 countries are good representatives to. Comparison of maximum entropy and higherorder entropy.
A simple introduction to maximum entropy models for. Correcting sample selection bias in maximum entropy density. The idea of the maximum entropy markov model memm is to make use of both the hmm framework to predict sequence labels given an observation sequence, but incorporating the multinomial logistic regression aka maximum entropy, which gives freedom in the type and number of features one can extract from the observation sequence. Generalized maximum entropy estimation of discrete. Hodge1,2 1battelle center for mathematical medicine, research institute at the nationwide childrens hospital, 700 childrens drive, oh 43205. Software eric ristads maximum entropy modelling toolkit this link is to the maximum entropy modeling toolkit, for parameter estimation and prediction for maximum entropy models in discrete domains. Entropy is a concept that originated in thermodynamics, and later, via statistical mechanics, motivated entire branches of information theory, statistics, and machine learning. The method is based on choosing the spectrum which corresponds to the most random or the most unpredictable time series whose autocorrelation function agrees with the known values.
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