Apprentissage de Concept a partir d'Exemples (tres) Ambigus

National audienceDans cet article nous explorons l'incompletude des donnees dans le cadre de l'apprentissage de concepts propositionnels. Nous suivons l'idee de H. Hirsh qui etend le paradigme de l'espace des versions : dans cette extension une hypothese doit etre compatible (dans un sens a definir au cas par cas) avec toutes les informations relatives aux exemples. Nous proposons une representation de ces informations qui rend non seulement compte de situations ou les donnes sont manquantes mais aussi de situations plus generales d'ambiguite dans lesquelles l'exemple est cache au sein d'un ensemble d'instances virtuelles. Nous presentons un nouvel algorithme, LEa, qui apprend un concept DNF (monotone) existentiel a partir d'un ensemble d'exemples ambigus. Nous comparons LEa a J48 et Naive Bayes sur des problemes usuels rendus incomplets a divers degres. Résumé français : Dans cet article nous explorons l'incompletude des donnees dans le cadre de l'apprentissage de concepts propositionnels. Nous suivons l'idee de H. Hirsh qui etend le paradigme de l'espace des versions : dans cette extension une hypothese doit etre compatible (dans un sens a definir au cas par cas) avec toutes les informations relatives aux exemples. Nous proposons une representation de ces informations qui rend non seulement compte de situations ou les donnes sont manquantes mais aussi de situations plus generales d'ambiguite dans lesquelles l'exemple est cache au sein d'un ensemble d'instances virtuelles. Nous presentons un nouvel algorithme, LEa, qui apprend un concept DNF (monotone) existentiel a partir d'un ensemble d'exemples ambigus. Nous comparons LEa a J48 et Naive Bayes sur des problemes usuels rendus incomplets a divers degres

An elementary chromatic reduction for gain graphs and special hyperplane arrangements

A gain graph is a graph whose edges are labelled invertibly by "gains" from a group. "Switching" is a transformation of gain graphs that generalizes conjugation in a group. A "weak chromatic function" of gain graphs with gains in a fixed group satisfies three laws: deletion-contraction for links with neutral gain, invariance under switching, and nullity on graphs with a neutral loop. The laws lead to the "weak chromatic group" of gain graphs, which is the universal domain for weak chromatic functions. We find expressions, valid in that group, for a gain graph in terms of minors without neutral-gain edges, or with added complete neutral-gain subgraphs, that generalize the expression of an ordinary chromatic polynomial in terms of monomials or falling factorials. These expressions imply relations for chromatic functions of gain graphs. We apply our relations to some special integral gain graphs including those that correspond to the Shi, Linial, and Catalan arrangements, thereby obtaining new evaluations of and new ways to calculate the zero-free chromatic polynomial and the integral and modular chromatic functions of these gain graphs, hence the characteristic polynomials and hypercubical lattice-point counting functions of the arrangements. We also calculate the total chromatic polynomial of any gain graph and especially of the Catalan, Shi, and Linial gain graphs.Comment: 31 page

Le bridge, nouveau défi de l’intelligence artificielle ?

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Boosting a Bridge Artificial Intelligence

Bridge is an incomplete information game which is complex both for humans and for computer bridge programs. The purpose of this paper is to present our work related to the adaptation to bridge of a recent methodology used for boosting game Artificial Intelligence (AI) by seeking a random seed, or a probability distribution on random seeds, better than the others on a particular game. The bridge AI Wbridge5 developed by Yves Costel has been boosted with the best seed found on the outcome of these experiments and has won the World Computer-Bridge Championship in September 2016

Concept Learning from (Very) Ambiguous Examples

International audienceWe investigate here concept learning from incomplete examples, denoted here as ambiguous. We start from the learning from interpretations setting introduced by L. De Raedt and then follow the informal ideas presented by H. Hirsh to extend the Version space paradigm to incomplete data: a hypothesis has to be compatible with all pieces of information provided regarding the examples. We propose and experiment an algorithm that given a set of ambiguous examples, learn a concept as an existential monotone DNF, We show that 1) boolean concepts can be learned, even with very high incompleteness level as long as enough information is provided, and 2) monotone, non monotone DNF (i.e. including negative literals), and attribute-value hypotheses can be learned that way, using an appropriate background knowledge. We also show that a clever implementation, based on a multi-table representation is necessary to apply the method with high levels of incompleteness

Bijections between affine hyperplane arrangements and valued graphs

galacInternational audienceWe show new bijective proofs of previously known formulas for the number of regions of some deformations of the braid arrangement, by means of a bijection between the no-broken-circuit sets of the corresponding integral gain graphs and some kinds of labelled binary trees. This leads to new bijective proofs for the Shi, Catalan, and similar hyperplane arrangements