Polynomial-Time Exact MAP Inference on Discrete Models with Global Dependencies

TL;DR

This paper introduces a novel polynomial-time exact MAP inference method for discrete models with global dependencies, overcoming traditional limitations related to graph complexity and enabling efficient inference in previously intractable scenarios.

Contribution

It extends existing frameworks for efficient inference by allowing finer interactions between model energy and global factors, and introduces a new graph transformation technique for improved efficiency.

Findings

Demonstrates the method's effectiveness on practical problems including previously intractable cases.

Provides a new graph transformation technique via node cloning ensuring polynomial runtime.

Achieves better theoretical guarantees compared to previous approaches.

Abstract

Considering the worst-case scenario, junction tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a corresponding MRF to be bounded strongly limiting the range of admissible applications. In fact, many practical problems in the area of structured prediction require modelling of global dependencies by either directly introducing global factors or enforcing global constraints on the prediction variables. That, however, always results in a fully-connected graph making exact inference by means of this algorithm intractable. Previous work [1]-[4] focusing on the problem of loss-augmented inference has demonstrated how efficient inference can be performed on models with specific global factors representing non-decomposable loss functions within the training regime of SSVMs. In this paper, we extend the framework for an efficient exact inference proposed in in [3] by allowing much finer interactions between the energy of the core model and the sufficient statistics of the global terms with no additional computation costs. We demonstrate the usefulness of our method in several use cases, including one that cannot be handled by any of the previous approaches. Finally, we propose a new graph transformation technique via node cloning which ensures a polynomial run-time for solving our target problem independently of the form of a corresponding clique tree. This is important for the efficiency of the main algorithm and greatly improves upon the theoretical guarantees of the previous works.