A Phase Transition-Based Perspective on Multiple Instance Kernels
Romaric Gaudel, Michele Sebag and Antoine Cornuéjols
In: ILP-07, 19-21 June 2007, Corvallis, Oregon.
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 thereof. 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 \MISVM\ 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 \MISVM\ error rates are high. An interpretation for these results is proposed.