PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Phase transition within grammatical inference
Nicolas Pernot, Antoine Cornuéjols and Michele Sebag
In: IJCAI 2005, 30 Jul - 05 Aug 2005, Edinburgh, Scotland.

Abstract

It is now well-known that the feasibility of inductive learning is ruled by statistical properties linking the empirical risk minimization principle and the ``capacity'' of the hypothesis space. The discovery, a few years ago, of a phase transition phenomenon in inductive logic programming proves that other fundamental characteristics of the learning problems may similarly affect the very possibility of learning under very general conditions. Our work examines the case of grammatical inference. We show that while there is no phase transition when considering the whole hypothesis space, there is a much more severe ``gap'' phenomenon affecting the effective search space of standard grammatical induction algorithms for deterministic finite automata (DFA). Focusing on the search heuristics of the \textsc{Rpni} and \textsc{Red-Blue} algorithms, we show that they overcome this problem to some extent, but that they are subject to overgeneralization. The paper last suggests some directions for new generalization operators, suited to this Phase Transition phenomenon.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:1521
Deposited By:Antoine Cornuéjols
Deposited On:28 November 2005