Hybrid SRL with Optimization Modulo Theories
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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 statistical-relational 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) First-Order Logic (FOL) as a description language, and on MAX-SAT 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 Boolean-numerical 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.
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