Bridging logic and kernel machines |
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Authors: | Michelangelo Diligenti Marco Gori Marco Maggini Leonardo Rigutini |
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Affiliation: | 1. Dipartimento di Ingegneria dell??Informazione, Universit?? di Siena, Siena, Italy
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Abstract: | We propose a general framework to incorporate first-order logic (FOL) clauses, that are thought of as an abstract and partial
representation of the environment, into kernel machines that learn within a semi-supervised scheme. We rely on a multi-task
learning scheme where each task is associated with a unary predicate defined on the feature space, while higher level abstract
representations consist of FOL clauses made of those predicates. We re-use the kernel machine mathematical apparatus to solve
the problem as primal optimization of a function composed of the loss on the supervised examples, the regularization term,
and a penalty term deriving from forcing real-valued constraints deriving from the predicates. Unlike for classic kernel machines,
however, depending on the logic clauses, the overall function to be optimized is not convex anymore. An important contribution
is to show that while tackling the optimization by classic numerical schemes is likely to be hopeless, a stage-based learning
scheme, in which we start learning the supervised examples until convergence is reached, and then continue by forcing the
logic clauses is a viable direction to attack the problem. Some promising experimental results are given on artificial learning
tasks and on the automatic tagging of bibtex entries to emphasize the comparison with plain kernel machines. |
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Keywords: | |
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