Hybrid SRL with Optimization Modulo Theories
Abstract
Generally speaking, the goal of constructive learning could be seen as, given an example set of structured objects, to generate novel objects with similar properties. From a statisticalrelational learning (SRL) viewpoint, the task can be interpreted as a constraint satisfaction problem, i.e. the generated objects must obey a set of soft constraints, whose weights are estimated from the data. Traditional SRL approaches rely on (finite) FirstOrder Logic (FOL) as a description language, and on MAXSAT solvers to perform inference. Alas, FOL is unsuited for con structive problems where the objects contain a mixture of Boolean and numerical variables. It is in fact difficult to implement, e.g. linear arithmetic constraints within the language of FOL. In this paper we propose a novel class of hybrid SRL methods that rely on Satisfiability Modulo Theories, an alternative class of for mal languages that allow to describe, and reason over, mixed Booleannumerical objects and constraints. The resulting methods, which we call Learning Mod ulo Theories, are formulated within the structured output SVM framework, and employ a weighted SMT solver as an optimization oracle to perform efficient in ference and discriminative max margin weight learning. We also present a few examples of constructive learning applications enabled by our method.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.4354
 Bibcode:
 2014arXiv1402.4354T
 Keywords:

 Computer Science  Machine Learning;
 Statistics  Machine Learning