Conditions for Unnecessary Logical Constraints in Kernel Machines

TL;DR

This paper extends the concept of support vectors to support constraints in kernel machines, providing criteria to identify and remove unnecessary logical constraints without affecting the optimal solution.

Contribution

It introduces the notion of support constraints, offers criteria for their removal, and analyzes logical constraints in Lukasiewicz logic to improve learning efficiency.

Findings

Support constraints can be identified and removed without changing the optimal solution.

Theoretical criteria for unnecessary constraints are established and exemplified.

Logical constraints in Lukasiewicz logic are effectively analyzed for their necessity.

Abstract

A main property of support vector machines consists in the fact that only a small portion of the training data is significant to determine the maximum margin separating hyperplane in the feature space, the so called support vectors. In a similar way, in the general scheme of learning from constraints, where possibly several constraints are considered, some of them may turn out to be unnecessary with respect to the learning optimization, even if they are active for a given optimal solution. In this paper we extend the definition of support vector to support constraint and we provide some criteria to determine which constraints can be removed from the learning problem still yielding the same optimal solutions. In particular, we discuss the case of logical constraints expressed by Lukasiewicz logic, where both inferential and algebraic arguments can be considered. Some theoretical results that characterize the concept of unnecessary constraint are proved and explained by means of examples.