Finding More Relevance: Propagating Similarity on Markov Random Field for Image Retrieval

To effectively retrieve objects from large corpus with high accuracy is a challenge task. In this paper, we propose a method that propagates visual feature level similarities on a Markov random field (MRF) to obtain a high level correspondence in image space for image pairs. The proposed correspondence between image pair reflects not only the similarity of low-level visual features but also the relations built through other images in the database and it can be easily integrated into the existing bag-of-visual-words(BoW) based systems to reduce the missing rate. We evaluate our method on the standard Oxford-5K, Oxford-105K and Paris-6K dataset. The experiment results show that the proposed method significantly improves the retrieval accuracy on three datasets and exceeds the current state-of-the-art retrieval performance

Quantum Graphical Models and Belief Propagation

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersely-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.Comment: 58 pages, 9 figure

Reweighted belief propagation and quiet planting for random K-SAT

We study the random K-satisfiability problem using a partition function where each solution is reweighted according to the number of variables that satisfy every clause. We apply belief propagation and the related cavity method to the reweighted partition function. This allows us to obtain several new results on the properties of random K-satisfiability problem. In particular the reweighting allows to introduce a planted ensemble that generates instances that are, in some region of parameters, equivalent to random instances. We are hence able to generate at the same time a typical random SAT instance and one of its solutions. We study the relation between clustering and belief propagation fixed points and we give a direct evidence for the existence of purely entropic (rather than energetic) barriers between clusters in some region of parameters in the random K-satisfiability problem. We exhibit, in some large planted instances, solutions with a non-trivial whitening core; such solutions were known to exist but were so far never found on very large instances. Finally, we discuss algorithmic hardness of such planted instances and we determine a region of parameters in which planting leads to satisfiable benchmarks that, up to our knowledge, are the hardest known.Comment: 23 pages, 4 figures, revised for readability, stability expression correcte

Joint Training of a Convolutional Network and a Graphical Model for Human Pose Estimation

This paper proposes a new hybrid architecture that consists of a deep Convolutional Network and a Markov Random Field. We show how this architecture is successfully applied to the challenging problem of articulated human pose estimation in monocular images. The architecture can exploit structural domain constraints such as geometric relationships between body joint locations. We show that joint training of these two model paradigms improves performance and allows us to significantly outperform existing state-of-the-art techniques

Maximum-a-posteriori estimation with Bayesian confidence regions

Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a result, while most modern mathematical imaging methods produce impressive point estimation results, they are generally unable to quantify the uncertainty in the solutions delivered. This paper presents a new general methodology for approximating Bayesian high-posterior-density credibility regions in inverse problems that are convex and potentially very high-dimensional. The approximations are derived by using recent concentration of measure results related to information theory for log-concave random vectors. A remarkable property of the approximations is that they can be computed very efficiently, even in large-scale problems, by using standard convex optimisation techniques. In particular, they are available as a by-product in problems solved by maximum-a-posteriori estimation. The approximations also have favourable theoretical properties, namely they outer-bound the true high-posterior-density credibility regions, and they are stable with respect to model dimension. The proposed methodology is illustrated on two high-dimensional imaging inverse problems related to tomographic reconstruction and sparse deconvolution, where the approximations are used to perform Bayesian hypothesis tests and explore the uncertainty about the solutions, and where proximal Markov chain Monte Carlo algorithms are used as benchmark to compute exact credible regions and measure the approximation error