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Register a new userMessage Passing Algorithms for Sparse Network Alignment
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Network alignment generalizes and unifies several approaches for forming a matching or alignment between the vertices of two graphs. We study a mathematical programming framework for network alignment problem and a sparse variation of it where only a small number of matches between the vertices of the two graphs are possible. We propose a new message passing algorithm that allows us to compute, very efficiently, approximate solutions to the sparse network alignment problems with graph sizes as large as hundreds of thousands of vertices. We also provide extensive simulations comparing our algorithms with two of the best solvers for network alignment problems on two synthetic matching problems, two bioinformatics problems, and three large ontology alignment problems including a multilingual problem with a known labeled alignment.
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Maximum A Posteriori inference in graphical models is often solved via message-passing algorithms, such as the junction-tree algorithm, or loopy belief-propagation. The exact solution to this problem is well known to be exponential in the size of the models maximal cliques after it is triangulated, while approximate inference is typically exponential in the size of the models factors. In this paper, we take advantage of the fact that many models have maximal cliques that are larger than their constituent factors, and also of the fact that many factors consist entirely of latent variables (i.e., they do not depend on an observation). This is a common case in a wide variety of applications, including grids, trees, and ring-structured models. In such cases, we are able to decrease the exponent of complexity for message-passing by 0.5 for both exact and approximate inference.
We consider a broad class of Approximate Message Passing (AMP) algorithms defined as a Lipschitzian functional iteration in terms of an $ntimes n$ random symmetric matrix $A$. We establish universality in noise for this AMP in the $n$-limit and validate this behavior in a number of AMPs popularly adapted in compressed sensing, statistical inferences, and optimizations in spin glasses.
Sparse Bayesian learning (SBL) can be implemented with low complexity based on the approximate message passing (AMP) algorithm. However, it does not work well for a generic measurement matrix, which may cause AMP to diverge. Damped AMP has been used for SBL to alleviate the problem at the cost of reducing convergence speed. In this work, we propose a new SBL algorithm based on structured variational inference, leveraging AMP with a unitary transformation (UAMP). Both single measurement vector and multiple measurement vector problems are investigated. It is shown that, compared to state-of-the-art AMP-based SBL algorithms, the proposed UAMP-SBL is more robust and efficient, leading to remarkably better performance.
Due to the massive number of devices in the M2M communication era, new challenges have been brought to the existing random-access (RA) mechanism, such as severe preamble collisions and resource block (RB) wastes. To address these problems, a novel sparse message passing (SMP) algorithm is proposed, based on a factor graph on which Bernoulli messages are updated. The SMP enables an accurate estimation on the activity of the devices and the identity of the preamble chosen by each active device. Aided by the estimation, the RB efficiency for the uplink data transmission can be improved, especially among the collided devices. In addition, an analytical tool is derived to analyze the iterative evolution and convergence of the SMP algorithm. Finally, numerical simulations are provided to verify the validity of our analytical results and the significant improvement of the proposed SMP on estimation error rate even when preamble collision occurs.
Tracking an unknown number of targets based on multipath measurements provided by an over-the-horizon radar (OTHR) network with a statistical ionospheric model is complicated, which requires solving four subproblems: target detection, target tracking, multipath data association and ionospheric height identification. A joint solution is desired since the four subproblems are highly correlated, but suffering from the intractable inference problem of high-dimensional latent variables. In this paper, a unified message passing approach, combining belief propagation (BP) and mean-field (MF) approximation, is developed for simplifying the intractable inference. Based upon the factor graph corresponding to a factorization of the joint probability distribution function (PDF) of the latent variables and a choice for a separation of this factorization into BP region and MF region, the posterior PDFs of continuous latent variables including target kinematic state, target visibility state, and ionospheric height, are approximated by MF due to its simple MP update rules for conjugate-exponential models. With regard to discrete multipath data association which contains one-to-one frame (hard) constraints, its PDF is approximated by loopy BP. Finally, the approximated posterior PDFs are updated iteratively in a closed-loop manner, which is effective for dealing with the coupling issue among target detection, target tracking, multipath data association, and ionospheric height identification. Meanwhile, the proposed approach has the measurement-level fusion architecture due to the direct processing of the raw multipath measurements from an OTHR network, which is benefit to improving target tracking performance. Its performance is demonstrated on a simulated OTHR network multitarget tracking scenario.
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