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Topic: Maximum entropy

	Amazon.com: Maximum Entropy and Bayesian Methods (Fundamental Theories of Physics): Books: John Skilling (Site not responding. Last check: 2007-11-02)
		Maximum Entropy, with its emphasis on optimally selected results, is an important part of this.
		The annual Maximum Entropy Workshops have become the principal focus of developments in the field, and which capture the imaginative research that defines the state of the art in the subject.
		Maximum Entropy and Bayesian Methods (Fundamental Theories of Physics) by W.T. Grandy Jr.
	www.amazon.com /Maximum-Entropy-Bayesian-Fundamental-Theories/dp/0792302249 (928 words)

	Data Reconstruction with a Maximum Entropy Technique (Site not responding. Last check: 2007-11-02)
		Maximum entropy methods accomplish this by determining the least biased image consistent with the constraints of the problem.
		The entropy is a measure that assigns a positive weight to all possible configurations not excluded by the given information.
		Unlike other methods, such as maximum likelihood, this maximum entropy method returns a unique solution even for ill-posed problems in which the number of unknown variables is greater than the number of data points.
	www.astro.ufl.edu /~hueckst/VSEP_REPORT/r.hueckst.html (2013 words)

	Morgaine LeFaye » Blog Archive » Maximum entropy modeling (Site not responding. Last check: 2007-11-02)
		The principle of maximum entropy is a method for analysing the available information in order to determine a unique epistemic probability distribution.
		The principle of maximum entropy can be seen as a generalization of the classical principle of indifference, also known as the principle of insufficient reason.
		The principle of maximum entropy has origins in statistical thermodynamics, is related to information theory and has been applied to pattern recognition tasks such as language modeling and text classification.
	blog.morgaine-lefaye.net /archives/2005/02/14/21.41.18 (1433 words)

	Energy, Entropy, Economics, and Ecology
		Additionally, suitable economic and cultural forms of "entropy" presumably need to be added to the picture—but the biological systems within which economies function (or fail to be functional) fall in the arena of evolutionary ecology, and this is the domain of the entropy concept into which an economic entropy concept should be fitted.
		Entropy can be thought of as a measure of how close a system is to equilibrium; it can also be thought of as a measure of the disorder in the system.
		Entropy change in such a system is given by the equation deS - djS < 0); that is, the entropy produced by irreversible processes within the system is shifted into the environment.
	www.dieoff.com /page17.htm (9313 words)

	EVOLUTION, ENTROPY AND WORK
		There may be metaphors for entropy, which may be useful in information theory or in other approaches to understanding complex systems, but if we label these with the word "entropy," which has a very specific physical meaning, we lose sight of any real value of the term.
		In this case, the decrease of Q(h) by W in the numerator of the first term is exactly proportional to the smaller denominator represented by the lower temperature reservoir, T(c), and the terms cancel in Equation [6].
		The maximum possible increase in entropy for a given system is found when all of the thermal energy flowing in as heat from the high temperature source, is also flowing out as heat to the low temperature sink.
	www.geoman.com /jim/entropy.html (4350 words)

	Re: Please describe how P. J. Burg's maximum entropy method works.
		By saying the least possible, the entropy is the maximum possible.
		The effect of Burg's Maximum Entropy Method, therefore, is that high resolution is obtained in the spectrum estimate (thanks to the parametric model for the signal generator) but we haven't fooled ourselves by asserting more information than is actually observable in the data.
		For signal power spectra, entropy is estimated by measuring the "flatness" of the spectrum.
	www.madsci.org /posts/archives/1997-05/864012045.Eg.r.html (2019 words)

	The OpenNLP Maxent Homepage
		Maximum entropy modeling is a framework for integrating information from many heterogeneous information sources for classification.
		Choosing the maximum entropy model is motivated by the desire to preserve as much uncertainty as possible.
		While the authors of this implementation of maximum entropy are generally interested using maxent models in natural language processing, the framework is certainly quite general and useful for a much wider variety of fields.
	maxent.sourceforge.net /about.html (670 words)

	Maximum Entropy
		By varying the complexity parameters (such as the number of clusters in the mixture model, the size of the AD tree or the upper limit on the frequency of itemsets used in learning of the maximum entropy model) we obtained multiple points on the graphs for some of the models.
		The maximum entropy models are still able to offer high accuracy and require less memory than AD trees but the online time requirements for them grow exponentially with the query size.
		Showed that the maximum entropy approach allows for substantial accuracy gains compared to the independence and the Chow-Liu model at the expense of increased processing time.
	www.datalab.uci.edu /projects/maxent (663 words)

	Maximum Entropy
		In ``A maximum entropy approach to natural language processing'' (Computational Linguistics 22:1, March 1996), the appendix describes an approach to computing the gain of a single feature f.
		This link is to the Maximum Entropy Modeling Toolkit, for parameter estimation and prediction for maximum entropy models in discrete domains.
		We present a maximum-likelihood approach for automatically constructing maximum entropy models and describe how to implement this approach efficiently, using as examples several problems in natural language processing.
	www.cs.cmu.edu /~aberger/maxent.html (932 words)

	Maximum Entropy
		The principle of maximum entropy originated in the last century with Gibbs and was re-constructed in its modern, broader form by Jaynes.
		Maximum Entropy and Bayesian Spectral Analysis and Estimation, edited by C.R. Smith and G.J. Erickson (Reidel, Dordrecht, Holland, 1987).
		Maximum Entropy and Bayesian Methods, Seattle, 1991, edited by C.R. Smith, G.J. Erickson and P.O. Neudorfer (Kluwer, Dordrecht, Holland, 1992).
	asuwlink.uwyo.edu /~wtg/infophys/node12.html (752 words)

	Citebase - Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory (Site not responding. Last check: 2007-11-02)
		Although Tops\oe described this connection for the Shannon entropy over 20 years ago, it does not appear to be widely known even in that important special case.
		We indicate how an appropriate generalized definition of entropy can be associated with such a problem, and we show that, subject to certain regularity conditions, the above-mentioned duality continues to apply in this extended context.
		Shimony, A. The status of the principle of maximum entropy.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0410076 (1177 words)

	Maximum Entropy Fundamentals (Site not responding. Last check: 2007-11-02)
		This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy.
		The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy".
		This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory.
	www.hsc.wvu.edu /sop/compchem/mdpi/entropy/htm/e3030191.htm (404 words)

	Materials Fatigue Life Distribution: A Maximum Entropy Approach
		A rational probability distribution for materials fatigue life is proposed using the Maximum Entropy Principle (MEP) and the sample information available.
		It has been shown that this distribution is most naturally a truncated normal distribution; The expression of the distribution as well as the relationships between the distribution parameters and the maximum entropy coefficients (or Lagrangian multipliers) is given explicitly.
		It is further shown that the maximum entropy estimators (MEE) are equivalent to the classical maximum likelihood estimators (MLE) and the moment estimators (ME) provided that proper sample statistics are chosen as the approximations of the population parameters.
	www.astm.org /JOURNALS/TESTEVAL/PAGES/300.htm (212 words)

	entropy - Definitions from Dictionary.com
		(in cosmology) a hypothetical tendency for the universe to attain a state of maximum homogeneity in which all matter is at a uniform temperature (heat death).
		The amount of entropy is often thought of as the amount of disorder in a system.
		The entropy of a system is related to the amount of information it contains.
	dictionary.reference.com /browse/entropy (789 words)

	The Principle of Maximum Entropy
		The Principle of Maximum Entropy states: When one has only partial information about the possible outcomes one should choose the probabilities so as to maximize the uncertainty about the missing information, as shown by Jaynes [8].
		By applying the principle of maximum entropy, one obtains the most random distribution subject to the satisfaction of the given constraints.
		The principle of Maximum Entropy provides that if there are n possible outcomes then, in the absence of additional information, the outcomes should be presumed to have equal probabilities.
	me.queensu.ca /people/sellens/research/sprayFlow/preusser/diplomar/node11.html (377 words)

	Maximum Entropy Modeling Using SharpEntropy - The Code Project - C# Libraries
		Presents a Maximum Entropy modeling library, and discusses its usage, with the aid of two examples: a simple example of predicting outcomes, and an English language tokenizer.
		Maximum entropy modeling is a general-purpose machine learning technique originally developed for statistical physics, but which has been employed in a wide variety of fields, including computer vision and natural language processing.
		The maximum entropy method follows the principle of “maximizing entropy” — that is, it chooses the model that takes account of all the facts available in the sample data but otherwise preserves as much uncertainty as possible.
	www.codeproject.com /cs/library/sharpentropy.asp (2479 words)

	The Law of Maximum Entropy Production: Dissolving the Postulates of Incommensurability
		The classical statement of the second law says that entropy will be maximized, or potentials minimized, but it does not ask or answer the question of which out of available paths a system will take to accomplish this end.
		The second law says only that entropy is maximized (or potentials are minimized), while the law of maximum entropy production says it is maximized at the fastest rate given the constraints.
		The point is that no matter what the specific conditions or the number of paths or drains, the system will automatically select the assembly of paths from among those otherwise available so as to get the system to the final state, to minimize or drain the potential, at the fastest rate given the constraints.
	members.tripod.com /spacetimenow/DarwinsDangerous23.html (624 words)

	Maximum Entropy Modeling (Site not responding. Last check: 2007-11-02)
		Furthermore, this unique solution is also the solution to the following dual problem: Maximize the log probability (2) on the training data using the model (4).
		In this formulation of the problem, it is easier to see that there exists exactly one maximum, because (2) is a sum of convex functions and therefore also convex.
		A second desirable property of the discussed model is that effective algorithms are known that compute the global maximum of the log probability (2) given a training set.
	www-i6.informatik.rwth-aachen.de /~keysers/Pubs/DAGM2002/node3.html (321 words)

	Maximum Entropy Models
		Maximum Entropy as a Special Case of Minimum Description Length Criterion.
		Maximum Entropy Techniques for Exploiting Syntactic, Semantic and Collocational Dependencies in Language Modeling.
		Approximate maximum entropy joint feature inference consistent with arbitrary lower order probability constraints: application to statistical classification.
	ciir.cs.umass.edu /~fuchun/readlist_all/readlist/node11.html (397 words)

	Maximum Entropy
		In ``A maximum entropy approach to natural language processing'' (Computational Linguistics 22:1, March 1996), the appendix describes an approach to computing the gain of a single feature f.
		The concept of maximum entropy can be traced back along multiple threads to Biblical times.
		Instead, we apply the principle of Maximum Entropy (ME).
	www-2.cs.cmu.edu /~aberger/maxent.html (932 words)

	Maximum Entropy Elements in the Intersection of an AffineSpace and the Cone of Positive Definite Matrices
		Maximum Entropy Elements in the Intersection of an AffineSpace and the Cone of Positive Definite Matrices
		Maximum Entropy Elements in the Intersection of an Affine Space and the Cone of Positive Definite Matrices:SIAM Journal on Matrix Analysis and Applications Vol.
		This matrix $F$ appears as the maximizer of a certain entropy function.
	epubs.siam.org /sam-bin/dbq/article/24354 (174 words)

	Maximum Entropy Modeling
		Maximum Entropy Modeling has been successfully applied to Computer Vision, Spatial Physics, Natural Language Processing and many other fields.
		A maximum entropy estimator with GIS, IIS and L-BFGS algorithms.
		Stanford Classifer is another open source implementation of Maximum Entropy Model in java, suitable for NLP tagging and parsing tasks.
	homepages.inf.ed.ac.uk /s0450736/maxent.html (1182 words)

	Maximum Entropy Models For Natural Language Ambiguity Resolution - Ratnaparkhi (ResearchIndex) (Site not responding. Last check: 2007-11-02)
		We discuss the problems of sentence boundary detection, part-of-speech tagging, prepositional phrase attachment, natural language parsing, and text categorization under the maximum entropy framework.
		Ratnaparkhi, Maximum Entropy Models for Natural Language Ambiguity Resolution, Ph.D. thesis, University of Pennsylvania, Philadelphia, PA, 1998.
		76 A maximum entropy approach to adaptive statistical language..
	citeseer.ist.psu.edu /ratnaparkhi98maximum.html (1127 words)

	Yet Another Machine Learning Blog » Maximum entropy and bayesian updating [Pierre Dangauthier]
		I was also thinking that the problem with that was the definition of priors, and that, in certain cincunstances, the Maximum entropy principle was helpful.
		Maximum entropy leads to P(X)= (1/6, 1/6, 1/6, 1/6, 1/6, 1/6).
		Dudik and R. Schapire, Maximum entropy distribution estimation with generalized regularization.
	emotion.inrialpes.fr /~dangauthier/blog/2006/04/26/maximum-entropy-and-bayesian-updating (1042 words)

	Maximum Entropy Methods
		Now, of course I believe that states of thermodynamic equilibrium are states of maximum entropy.
		51 (2005): 3322--3333 ["A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived.
		Most results in the literature are either focused on the minimum cross-entropy distribution or apply only to distributions with a bounded-volume support or address only equality constraints.
	www.cscs.umich.edu /~crshalizi/notebooks/max-ent.html (435 words)

	The Maximum Entropy Method (MEM)
		By contrast, the Maximum Entropy Method (MEM) is not procedural: the image selected is that which fits the data, to within the noise level, and also has maximum entropy.
		The authors' preferred justification defines the entropy as something which, when maximized, produces a positive image with a compressed range in pixel values.
		Image entropy thus defined is therefore not to be confused with a ``physical entropy'' (see Cornwell 1984a).
	www.cv.nrao.edu /~abridle/deconvol/node20.html (476 words)

	Maximum Entropy Online Resources (Site not responding. Last check: 2007-11-02)
		XIII International Workshop on Maximum Entropy and Bayesian Methods.
		An idiosyncratic hybrid page of Maximum Entropy and Space Time Algebra with general information about the Cambridge group.
		A Perl5 Module for Maximum Entropy Modeling by Hugo WL ter Doest.
	omega.albany.edu:8008 /maxent.html (124 words)

	Why maximize entropy?
		It is commonly accepted that if one is asked to select a distribution satisfying a bunch of constraints, and if these constraints do not determine a unique distribution, then one is best off picking the distribution having maximum entropy.
		But in the case we are talking about we have seen that for the maximum entropy distribution--that is, the least self-fulfilling distribution--the degree of verification doesn't depend on the q chosen.
		These are the sets from which it makes sense to pick the maximum entropy distribution.
	math.dartmouth.edu /~doyle/docs/whyme/whyme/whyme.html (1051 words)

	The Law of Maximum Entropy Production: Law of Spontaneous Order
		Now this becomes important only with the second part of the solution which is the answer to a question that did not arise in the Bertalanffy-Schroedinger-Prigogine discourse, nor was it a question that classical thermodynamics ever asked.
		The world, in short, is in the order production business because ordered flow produces entropy faster than disordered flow, and this, in most direct terms, provides the nomological basis for the reconciliation of the otherwise two incommensurable rivers.
		Rather than being anomalous with respect to, or somehow violating physical law, the "river that flows uphill" that characterizes the active epistemic dimension of the world is seen to be a direct manifestation of it.
	www.entropylaw.com /entropyproduction.html (493 words)

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