Efficient Sampling for Bipartite Matching Problems

Bipartite matching problems characterize many situations, ranging from ranking in information retrieval to correspondence in vision. Exact inference in real-world applications of these problems is intractable, making efficient approximation methods essential for learning and inference. In this paper we propose a novel sequential matching sampler based on a generalization of the Plackett-Luce model, which can effectively make large moves in the space of matchings. This allows the sampler to match the difficult target distributions common in these problems: highly multimodal distributions with well separated modes. We present experimental results with bipartite matching problems—ranking and image correspondence—which show that the sequential matching sampler efficiently approximates the target distribution, significantly outperforming other sampling approaches.