A Phase TRansition-Based Perspective on Multiple Instance KernelsReport as inadecuate




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1 LRI - Laboratoire de Recherche en Informatique 2 TANC - Algorithmic number theory for cryptology LIX - Laboratoire d-informatique de l-École polytechnique Palaiseau, Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7161 3 MIA-Paris - Mathématiques et Informatique Appliquées

Abstract : This paper is concerned with Relational Support Vector Machines, at the intersection of Support Vector Machines SVM and Inductive Logic Programming or Relational Learning. The so-called phase transition framework, originally developed for constraint satisfaction problems, has been extended to relational learning and it has provided relevant insights into the limitations and difficulties hereof. The goal of this paper is to examine relational SVMs and specifically Multiple Instance MI Kernels along the phase transition framework. A relaxation of the MI-SVM problem formalized as a linear programming problem LPP is defined and we show that the LPP satisfiability rate induces a lower bound on the MI-SVM generalization error. An extensive experimental study shows the existence of a critical region, where both LPP unsatisfiability and MI-SVM error rates are high. An interpretation for these results is proposed.





Author: Romaric Gaudel - Michèle Sebag - Antoine Cornuéjols -

Source: https://hal.archives-ouvertes.fr/



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