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Convex rank tests and semigraphoids
, 2008
"... Convex rank tests are partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. Each class consists of the linear extensions of a partially ordered set specified by data. ..."
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Cited by 18 (1 self)
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. Our methods refine existing rank tests of nonparametric statistics, such as the sign test and the runs test, and are useful for exploratory analysis of ordinal data. We establish a bijection between convex rank tests and probabilistic conditional independence structures known as semigraphoids
Three counterexamples on semigraphoids
"... Semigraphoids are combinatorial structures that arise in statistical learning theory. They are equivalent to convex rank tests and to polyhedral fans that coarsen the reflection arrangement of the symmetric group Sn. In this paper we resolve two problems on semigraphoids posed in Studen´y’s book [ ..."
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Cited by 11 (6 self)
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Semigraphoids are combinatorial structures that arise in statistical learning theory. They are equivalent to convex rank tests and to polyhedral fans that coarsen the reflection arrangement of the symmetric group Sn. In this paper we resolve two problems on semigraphoids posed in Studen´y’s book
Geometry of rank tests
 PROBABILISTIC GRAPHICAL MODELS (PGM 3
, 2006
"... We study partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. These permutations are the linear extensions of partially ordered sets specified by the data. Our metho ..."
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Cited by 4 (2 self)
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methods refine rank tests of nonparametric statistics, such as the sign test and the runs test, and are useful for the exploratory analysis of ordinal data. Convex rank tests correspond to probabilistic conditional independence structures known as semigraphoids. Submodular rank tests are classified
Abstracts of Workshop on Computational Algebraic Statistics, Theories and Applications
"... of the IASC on Computational Statistics & Data Analysis) held during December 58 in Yokohama, Japan. The objective of the workshop is to present new developments in algebraic methods in computational statistics. One of the main topics of the workshop is techniques of algebraic statistics, such ..."
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of the IASC on Computational Statistics & Data Analysis) held during December 58 in Yokohama, Japan. The objective of the workshop is to present new developments in algebraic methods in computational statistics. One of the main topics of the workshop is techniques of algebraic statistics, such as Groebner bases, Markov basis and symbolic computation. However we have many interesting talks of general interest on new developments in
Proceedings of the Third European Workshop on Probabilistic Graphical Models
, 2006
"... of workshops on probabilistic graphical models is to provide a discussion forum for researchers interested in this topic. The first European PGM workshop (PGM’02) was held in Cuenca, Spain in November 2002. It was a successful workshop and several of its participants expressed interest in having a b ..."
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of workshops on probabilistic graphical models is to provide a discussion forum for researchers interested in this topic. The first European PGM workshop (PGM’02) was held in Cuenca, Spain in November 2002. It was a successful workshop and several of its participants expressed interest in having a biennial European workshop devoted particularly to probabilistic graphical models. The second PGM workshop (PGM’04) was held in Leiden, the Netherlands in October 2004. It was also a success; more emphasis was put on collaborative work, and the participants also discussed how to foster cooperation between European research groups. There are two trends which can be observed in connection with PGM workshops. First, each workshop is held during an earlier month than the preceding one. Indeed, PGM’02 was held in November, PGM’04 in October and PGM’06 will be held in September. Nevertheless, I think this is a coincidence. The second trend is the increasing number of contributions (to be) presented. I would like to believe that this is not a coincidence, but an indication of increasing research interest in probabilistic graphical models. A total of 60 papers were submitted to PGM’06 and, after the reviewing and postreviewing phases, 41 of them were accepted for presentation at the workshop (21 talks, 20 posters) and
A UNIFYING FRAMEWORK FOR DISJUNCTIVE DATA CONSTRAINTS WITH APPLICATIONS TO REASONING UNDER UNCERTAINTY
, 2009
"... ..."
Algebraic Geometry of Bayesian Networks
, 2004
"... We develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry–statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of Bayesia ..."
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We develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry–statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification, in terms of primary decomposition of polynomial ideals, is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties. Moreover, a complete algebraic classification, in terms of generating sets of polynomial ideals, is given for Bayesian networks on at most three random variables and one hidden variable. The relevance of these results for model selection is discussed.
Results 1  10
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21