A Delayed Column Generation Strategy for Exact k-Bounded MAP Inference in Markov Logic Networks

TL;DR

This paper proposes a novel delayed column generation algorithm for efficient exact k-bounded MAP inference in Markov logic networks, enabling scalable solutions for complex graph matching problems.

Contribution

It introduces a new delayed column generation approach specifically designed for k-bounded MAP inference, improving computational efficiency.

Findings

Algorithm efficiently computes k-bounded MAP states in real-world problems

Approach outperforms traditional methods on graph matching tasks

Empirical results demonstrate scalability and effectiveness

Abstract

The paper introduces k-bounded MAP inference, a parameterization of MAP inference in Markov logic networks. k-Bounded MAP states are MAP states with at most k active ground atoms of hidden (non-evidence) predicates. We present a novel delayed column generation algorithm and provide empirical evidence that the algorithm efficiently computes k-bounded MAP states for meaningful real-world graph matching problems. The underlying idea is that, instead of solving one large optimization problem, it is often more efficient to tackle several small ones.