Efficient Semidefinite Branch-and-Cut for MAP-MRF Inference

We propose a Branch-and-Cut (B&C) method for solving general MAP-MRF inference problems. The core of our method is a very efficient bounding procedure, which combines scalable semidefinite programming (SDP) and a cutting-plane method for seeking violated constraints. In order to further speed up the computation, several strategies have been exploited, including model reduction, warm start and removal of inactive constraints. We analyze the performance of the proposed method under different settings, and demonstrate that our method either outperforms or performs on par with state-of-the-art approaches. Especially when the connectivities are dense or when the relative magnitudes of the unary costs are low, we achieve the best reported results. Experiments show that the proposed algorithm achieves better approximation than the state-of-the-art methods within a variety of time budgets on challenging non-submodular MAP-MRF inference problems.Comment: 21 page

Algorithmic statistics revisited

The mission of statistics is to provide adequate statistical hypotheses (models) for observed data. But what is an "adequate" model? To answer this question, one needs to use the notions of algorithmic information theory. It turns out that for every data string $x$ one can naturally define "stochasticity profile", a curve that represents a trade-off between complexity of a model and its adequacy. This curve has four different equivalent definitions in terms of (1)~randomness deficiency, (2)~minimal description length, (3)~position in the lists of simple strings and (4)~Kolmogorov complexity with decompression time bounded by busy beaver function. We present a survey of the corresponding definitions and results relating them to each other

Fusion of Head and Full-Body Detectors for Multi-Object Tracking

In order to track all persons in a scene, the tracking-by-detection paradigm has proven to be a very effective approach. Yet, relying solely on a single detector is also a major limitation, as useful image information might be ignored. Consequently, this work demonstrates how to fuse two detectors into a tracking system. To obtain the trajectories, we propose to formulate tracking as a weighted graph labeling problem, resulting in a binary quadratic program. As such problems are NP-hard, the solution can only be approximated. Based on the Frank-Wolfe algorithm, we present a new solver that is crucial to handle such difficult problems. Evaluation on pedestrian tracking is provided for multiple scenarios, showing superior results over single detector tracking and standard QP-solvers. Finally, our tracker ranks 2nd on the MOT16 benchmark and 1st on the new MOT17 benchmark, outperforming over 90 trackers.Comment: 10 pages, 4 figures; Winner of the MOT17 challenge; CVPRW 201