Beyond perturbation stability: LP recovery guarantees for MAP inference on noisy stable instances


Several works have shown that perturbation stable instances of the MAP inference problem in Potts models can be solved exactly using a natural linear programming (LP) relaxation. However, most of these works give few (or no) guarantees for the LP solutions on instances that do not satisfy the relatively strict perturbation stability definitions. In this work, we go beyond these stability results by showing that the LP approximately recovers the MAP solution of a stable instance even after the instance is corrupted by noise. This "noisy stable" model realistically fits with practical MAP inference problems: we design an algorithm for finding "close" stable instances, and show that several real-world instances from computer vision have nearby instances that are perturbation stable. These results suggest a new theoretical explanation for the excellent performance of this LP relaxation in practice.

Proceedings of the Twenty-Fourth International Conference on Artificial Intelligence and Statistics (AISTATS)
Hunter Lang
Hunter Lang
PhD Student

Hunter’s research focuses on understanding and improving the performance of machine learning algorithms in the wild, with particular applications in MAP inference for graphical models, stochastic optimization, and weak supervision.

David Sontag
David Sontag
Professor of EECS

My research focuses on advancing machine learning and artificial intelligence, and using these to transform health care.