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25
A model of community standards
, 2009
"... Comments welcome. I introduce a new model of community standards relevant to the judicial determination of obscenity. In the model, standards are defined as subjective judgments restricted only by a simple reasonableness condition. A set of individual standards is then methodically aggregated to for ..."
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Comments welcome. I introduce a new model of community standards relevant to the judicial determination of obscenity. In the model, standards are defined as subjective judgments restricted only by a simple reasonableness condition. A set of individual standards is then methodically aggregated to form the community standard. I define several axioms which reflect legal concerns expressed by the judiciary. The axioms require that the community standard (a) preserve unanimous agreements about the entire standard, (b) become more permissive when all individuals become more permissive, and not discriminate, ex ante, (c) between individuals and (d) between works. I then show that the only method which satisfies these properties is unanimity rule, in which a work is considered obscene if and only if all members of the community consider it to be obscene. I also consider several variants of the model and provide characterizations in these related models.
On semicube graphs
"... Eppstein [6] introduced semicube graphs as the key tool for efficient computation of the lattice dimension of a graph. In this paper it is shown that, roughly speaking, every graph can be realized as the semicube graph of somepartial cube. Semicube graphs of trees are studied in detail. In particul ..."
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Eppstein [6] introduced semicube graphs as the key tool for efficient computation of the lattice dimension of a graph. In this paper it is shown that, roughly speaking, every graph can be realized as the semicube graph of somepartial cube. Semicube graphs of trees are studied in detail. In particular the chromatic number, the independence number and the domination numberof semicube graphs of trees are determined in terms of related invariants of trees.
Toward optimal ordering of prediction tasks
 In SIAM International Conference on Data Mining (SDM
, 2009
"... Abstract Many applications involve a set of prediction tasks that must be accomplished sequentially through user interaction. If the tasks are interdependent, the order in which they are performed may have a significant impact on the overall performance of the prediction systems. However, manual sp ..."
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Abstract Many applications involve a set of prediction tasks that must be accomplished sequentially through user interaction. If the tasks are interdependent, the order in which they are performed may have a significant impact on the overall performance of the prediction systems. However, manual specification of an optimal order may be difficult when the interdependencies are complex, especially if the number of tasks is large, making exhaustive search intractable. This paper presents the first attempt at solving the optimal task ordering problem using an approximate formulation in terms of pairwise task order preferences, reducing the problem to the wellknown Linear Ordering Problem. We propose two approaches for inducing the pairwise task order preferences 1) a classifieragnostic approach based on conditional entropy that determines the prediction tasks whose correct labels lead to the least uncertainty for the remaining predictions, and 2) a classifierdependent approach that empirically determines which tasks are favored before others for better predictive performance. We apply the proposed solutions to two practical applications that involve computerassisted trouble report generation and document annotation, respectively. In both applications, the user fills up a series of fields and at each step, the system is expected to provide useful suggestions, which comprise the prediction (i.e. classification and ranking) tasks. Our experiments show encouraging improvements in predictive performance, as compared to approaches that do not take task dependencies into account.
Embedding topological median algebras in products of dendrons
 PROC. LONDON MATH. SOC
, 1989
"... Dendrons and their products admit a natural, continuous median operator. We prove that there exists a twodimensional metric continuum with a continuous median operator, for which there is no medianpreserving embedding in a product of finitely many dendrons. Our method involves ideas and results co ..."
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Dendrons and their products admit a natural, continuous median operator. We prove that there exists a twodimensional metric continuum with a continuous median operator, for which there is no medianpreserving embedding in a product of finitely many dendrons. Our method involves ideas and results concerning graph colouring and abstract convexity. The main result answers a question in [16] negatively, and is sharply contrasting with a result of Stralka [15] on embeddings of compact lattices.
Rules for Aggregating Information
, 2010
"... We present a model of information aggregation in which agents ’ information is represented through partitions over states of the world. We discuss three axioms, meet separability, upper unanimity, and nonimposition, and show that these three axioms characterize the class of oligarchic rules, which ..."
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We present a model of information aggregation in which agents ’ information is represented through partitions over states of the world. We discuss three axioms, meet separability, upper unanimity, and nonimposition, and show that these three axioms characterize the class of oligarchic rules, which combine all of the information held by a prespecified set of individuals. JEL classification: D70, D71, D72 1
Comparison of additive trees using . . .
, 2000
"... It has been postulated that existing species have been linked in the past in a way that can be described using an additive tree structure. Any such tree structure reflecting species relationships is associated with a matrix of distances between the species considered and called a distance matrix o ..."
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It has been postulated that existing species have been linked in the past in a way that can be described using an additive tree structure. Any such tree structure reflecting species relationships is associated with a matrix of distances between the species considered and called a distance matrix or a tree metric matrix. A circular order of elements of X corresponds to a circular (clockwise) scanning of the subset X of vertices of a tree drawn on a plane. This paper describes an optimal algorithm using circular orders to compare the topology of two trees given by their distance matrices. This algorithm allows us to compute the Robinson and Foulds topologic distance between two trees. It employs circular order tree reconstruction to compute an ordered bipartition table of the tree edges for both given distance matrices. These bipartition tables are then compared to determine the Robinson and Foulds topologic distance, known to be an important criterion of tree similarity. The described algorithm has optimal time complexity, requiring O(n performed on two nn distance matrices. It can be generalized to get another optimal algorithm, which enables the strict consensus tree of k unrooted trees, given their distance matrices, to be constructed in O(kn ) time.
Average consensus in numerical taxonomy and some generalizations
"... Abstract. This paper is devoted to the notion of average consensus together with some generalizations involving Lpnorms. We prove that finding one of these consensus dissimilarities out of a profile of dissimilarities is NPhard for ultrametrics, quasiutrametrics and proper dissimilarities satisfy ..."
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Abstract. This paper is devoted to the notion of average consensus together with some generalizations involving Lpnorms. We prove that finding one of these consensus dissimilarities out of a profile of dissimilarities is NPhard for ultrametrics, quasiutrametrics and proper dissimilarities satisfying the Bertrand and Janowitz kpoint inequality. The NPhardness of finding a consensus dissimilarity for a pyramid (also called an indexed pseudohierarchy) is also proved in the case of one of the two possible alternatives for generalized average consensus. Rsum. Ce papier est centr sur la notion de consensus moyen ainsi que sur quelquesunes de ses gnralisations concernant les normes Lp. Nous prouvons que trouver une dissimilarit consensus d’un profile de dissimilarits est NPcomplet pour les ulramtriques, les quasiultramtriques et les dissimilarits propres satifaisant la condition des kpoints de Bertrand et Janowitz. La NPcompltude de la recherche d’une dissimilarit consensus pour les pyramides (aussi appeles pseudohirarchies) est galement prouve pour une des deux gnralisations du consensus moyen.
Probabilistic MultiState SplitMerge Algorithm for Coupling Parameter Estimates
"... A new approach to finding good local maxima of the likelihood function based on synthesizing information from two local maxima is presented. We investigate the coupled EM algorithm (CoEM) for coupling local maxima solutions from two separate EM runs for the multinomial mixture model. The CoEM algori ..."
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A new approach to finding good local maxima of the likelihood function based on synthesizing information from two local maxima is presented. We investigate the coupled EM algorithm (CoEM) for coupling local maxima solutions from two separate EM runs for the multinomial mixture model. The CoEM algorithm probabilistically splits and merges multiple latent states based on conditional independence assumptions and is numerically shown to significantly improve on uncoupled EM or deterministic annealing (DAEM) parameter estimates.