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 relational learning or Inductive Logic Programming ILP. The so-called phase transition framework, primarily developed for constraint satisfaction problems CSP, has been extended to ILP, providing relevant insights into the limitations and difficulties thereof. The goal of this paper is to examine relational SVMs and specifically Multiple Instance-SVMs in the phase transition perspective. Introducing a relaxed CSP formalization of MI-SVMs, we first derive a lower bound on the MI-SVM generalization error in terms of the CSP satisfiability probability. Further, ample empirical evidence based on systematic experimentations demonstrates the existence of a unsatisfiability region, entailing the failure of MI-SVM approaches.

Author: Romaric Gaudel - Michèle Sebag - Antoine Cornuéjols -

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


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