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49
Maximum entropy Gaussian approximation for the number of integer points and volumes of polytopes
, 2009
"... We describe a maximum entropy approach for computing volumes and counting integer points in polyhedra. To estimate the number of points from a particular set X ⊂ R n in a polyhedron P ⊂ R n, by solving a certain entropy maximization problem, we construct a probability distribution on the set X such ..."
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We describe a maximum entropy approach for computing volumes and counting integer points in polyhedra. To estimate the number of points from a particular set X ⊂ R n in a polyhedron P ⊂ R n, by solving a certain entropy maximization problem, we construct a probability distribution on the set X such that a) the probability mass function is constant on the set P ∩X and b) the expectation of the distribution lies in P. This allows us to apply Central Limit Theorem type arguments to deduce computationally efficient approximations for the number of integer points, volumes, and the number of 01 vectors in the polytope. As an application, we obtain asymptotic formulas for volumes of multiindex transportation polytopes and for the number of multiway contingency tables.
A Logically Sound Method for Uncertain Reasoning With Quantified Conditionals
 IN PROCEEDINGS ECSQARU / FAPR97, LNAI 1244
, 1997
"... Conditionals play a central part in knowledge representation and reasoning. Describing certain relationships between antecedents and consequences by "ifthensentences" their range of expressiveness includes commonsense knowledge as well as scientific statements. In this paper, we presen ..."
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Cited by 4 (1 self)
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Conditionals play a central part in knowledge representation and reasoning. Describing certain relationships between antecedents and consequences by "ifthensentences" their range of expressiveness includes commonsense knowledge as well as scientific statements. In this paper, we present the principles of maximum entropy resp. of minimum crossentropy (MEprinciples) as a logically sound and practicable method for representing and reasoning with quantified conditionals. First the meaning of these principles is made clear by sketching a characterization from a completely conditionallogical point of view. Then we apply the techniques presented to derive MEdeduction schemes and illustrate them by examples in the second part of this paper.
Inference for Multiplicative Models
"... The paper introduces a generalization for known probabilistic models such as loglinear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture multiple forms of contextual independence between variables, includ ..."
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Cited by 4 (0 self)
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The paper introduces a generalization for known probabilistic models such as loglinear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture multiple forms of contextual independence between variables, including decision graphs and noisyOR functions. An inference algorithm for multiplicative models is provided and its correctness is proved. The complexity analysis of the inference algorithm uses a more refined parameter than the treewidth of the underlying graph, and shows the computational cost does not exceed that of the variable elimination algorithm in graphical models. The paper ends with examples where using the new models and algorithm is computationally beneficial.
WHAT DOES A RANDOM CONTINGENCY TABLE LOOK LIKE?
, 2008
"... Abstract. Let R = (r1,..., rm) and C = (c1,..., cn) be positive integer vectors such that r1 +... + rm = c1 +... + cn. We consider the set Σ(R, C) of nonnegative m × n integer matrices (contingency tables) with row sums R and column sums C as a finite probability space with the uniform measure. We ..."
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Abstract. Let R = (r1,..., rm) and C = (c1,..., cn) be positive integer vectors such that r1 +... + rm = c1 +... + cn. We consider the set Σ(R, C) of nonnegative m × n integer matrices (contingency tables) with row sums R and column sums C as a finite probability space with the uniform measure. We prove that a random table D ∈ Σ(R, C) is close with high probability to a particular matrix (“typical table”) Z defined as follows. We let g(x) = (x + 1) ln(x + 1) − x ln x for x ≥ 0 and let g(X) = P ij g(xij) for a nonnegative matrix X = (xij). Then g(X) is strictly concave and attains its maximum on the polytope of nonnegative m × n matrices X with row sums R and column sums C at a unique point, which we call the typical table Z.
Gedanken experimentation: an alternative to traditional system testing
 Information retrieval experiment
, 1981
"... Technological progress is generally brought about through a combination of intelligent theorizing, experimentation, and inspired tinkering. The technology of literature searching is no exception, and elements of all three have contributed to recent progress in the information retrieval field. Howeve ..."
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Technological progress is generally brought about through a combination of intelligent theorizing, experimentation, and inspired tinkering. The technology of literature searching is no exception, and elements of all three have contributed to recent progress in the information retrieval field. However, without disparaging in any way the research that has been carried out, it might fairly be observed that information retrieval is an area in which by the very nature of the subject matter the theory is thin and largescale experimentation cumbersome and often inconclusive. Perhaps, therefore, the time is ripe to start giving more attention to the third of the aforementioned alternatives, the scientifically disreputable but often surprisingly successful course of 'inspired tinkering'. I have in mind especially a kind of 'tinkering ' with retrieval system parameters through educated guesswork rather than careful fullscale experimentation. It involves the making of estimates, or 'guesstimates', based on very little datagathering or even on nothing more than human
Spatial Disaggregation of Agricultural Production Data by Maximum Entropy!
, 2002
"... In this paper we develop a dynamic dataconsistent way for estimating agricultural land use choices at a disaggregate level (districtlevel), using more aggregate data (regionallevel). The disaggregation procedure requires two steps. The first step consists in specifying and estimating a dynamic mo ..."
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In this paper we develop a dynamic dataconsistent way for estimating agricultural land use choices at a disaggregate level (districtlevel), using more aggregate data (regionallevel). The disaggregation procedure requires two steps. The first step consists in specifying and estimating a dynamic model of land use at the regionallevel. In the second step, we disaggregate outcomes of the aggregate model using maximum entropy (ME). The ME disaggregation procedure is applied to a sample of California data. The sample includes 6 districts located in Central Valley and 8
AUEB at TAC 2009
 In TAC 2009 Workshop, National Institute of Standards and Technology
, 2009
"... This paper describes AUEB’s participation in TAC 2009. Specifically, we participated in the textual entailment recognition track for which we used string similarity measures applied to shallow abstractions of the input sentences, and a Maximum Entropy classifier to learn how to combine the resulting ..."
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This paper describes AUEB’s participation in TAC 2009. Specifically, we participated in the textual entailment recognition track for which we used string similarity measures applied to shallow abstractions of the input sentences, and a Maximum Entropy classifier to learn how to combine the resulting features. We also exploited WordNet to detect synonyms and a dependency parser to measure similarity in the grammatical structure of T and H. 1
ACME: An Associative Classifier based on Maximum Entropy Principle
 In 16th International Conference on Algorithmic Learning Theory (ALT
"... Abstract. Recent studies in classification have proposed ways of exploiting the association rule mining paradigm. These studies have performed extensive experiments to show their techniques to be both efficient and accurate. However, existing studies in this paradigm either do not provide any theore ..."
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Abstract. Recent studies in classification have proposed ways of exploiting the association rule mining paradigm. These studies have performed extensive experiments to show their techniques to be both efficient and accurate. However, existing studies in this paradigm either do not provide any theoretical justification behind their approaches or assume independence between some parameters. In this work, we propose a new classifier based on association rule mining. Our classifier rests on the maximum entropy principle for its statistical basis and does not assume any independence not inferred from the given dataset. We use the classical generalized iterative scaling algorithm (GIS) to create our classification model. We show that GIS fails in some cases when itemsets are used as features and provide modifications to rectify this problem. We show that this modified GIS runs much faster than the original GIS. We also describe techniques to make GIS tractable for large feature spaces – we provide a new technique to divide a feature space into independent clusters each of which can be handled separately. Our experimental results show that our classifier is generally more accurate than the existing classification methods. 1
Matrices with prescribed row and column sums
 Linear Algebra Appl
"... Abstract. This is a survey of the recent progress and open questions on the structure of the sets of 01 and nonnegative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from the set, discrete versions of the BrunnMinkowski in ..."
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Abstract. This is a survey of the recent progress and open questions on the structure of the sets of 01 and nonnegative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from the set, discrete versions of the BrunnMinkowski inequality and the statistical dependence between row and column sums. 1.