Learning to Tag from Logic Constraints in Hyperlinked Environments

This paper presents a novel framework to integrate prior knowledge, represented as a collection of First Order Logic (FOL) clauses, into regularization over discrete domains. In particular, we consider tasks in which a set of items are connected to each other by given relationships yielding a graph, whose nodes correspond to the available objects, and it is required to estimate a set of functions defined on each node of the graph, given a small set of labeled nodes for each function. The available prior knowledge imposes a set of constraints among the function values. In particular, we consider background knowledge expressed as FOL clauses, whose predicates correspond to the functions and whose variables range over the nodes of the graph. These clauses can be converted into a set of constraints that can be embedded into a graph regularization schema. The experimental results evaluate the proposed technique on an image tagging task, showing how the proposed approach provides a significantly higher tagging accuracy than simple graph regularization.