LPQP for MAP: Putting LP Solvers to Better Use
This work addresses MAP inference, a key problem in machine learning for tasks like computer vision, by offering a novel relaxation that improves over standard LP methods, though it appears incremental as it builds on existing LP and QP frameworks.
The paper tackled the challenging problem of MAP inference for general energy functions by proposing a novel relaxation that penalizes the KL divergence between LP pairwise auxiliary variables and QP terms from unary products, resulting in algorithms that substantially improve over the LP relaxation in experiments on synthetic and real-world data.
MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation. We propose a novel MAP relaxation that penalizes the Kullback-Leibler divergence between the LP pairwise auxiliary variables, and QP equivalent terms given by the product of the unaries. We develop two efficient algorithms based on variants of this relaxation. The algorithms minimize the non-convex objective using belief propagation and dual decomposition as building blocks. Experiments on synthetic and real-world data show that the solutions returned by our algorithms substantially improve over the LP relaxation.