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- Mohsen Bayati, Andrea Montanari
- IEEE Transactions on Information Theory
- 2010

“Approximate message passing” (AMP) algorithms have proved to be effective in reconstructing sparse signals from a small number of incoherent linear measurements. Extensive numerical experiments further showed that their dynamics is accurately tracked by a simple one-dimensional iteration termed state evolution. In this paper, we provide… (More)

- Mohsen Bayati, Andrea Montanari
- IEEE Transactions on Information Theory
- 2012

We consider the problem of learning a coefficient vector x<sub>ο</sub> ∈ R<sup>N</sup> from noisy linear observation y = Ax<sub>o</sub> + ∈ R<sup>n</sup>. In many contexts (ranging from model selection to image processing), it is desirable to construct a sparse estimator x̂. In this case, a popular approach consists in solving an… (More)

- Mohsen Bayati, Devavrat Shah, Mayank Sharma
- IEEE Transactions on Information Theory
- 2008

Max-product "belief propagation" (BP) is an iterative, message-passing algorithm for finding the maximum a posteriori (MAP) assignment of a discrete probability distribution specified by a graphical model. Despite the spectacular success of the algorithm in many application areas such as iterative decoding and combinatorial optimization, which involve… (More)

- Mohsen Bayati, Devavrat Shah, Mayank Sharma
- Proceedings. International Symposium on…
- 2005

The max-product "belief propagation" algorithm is an iterative, local, message passing algorithm for finding the maximum a posteriori (MAP) assignment of a discrete probability distribution specified by a graphical model. Despite the spectacular success of the algorithm in many application areas such as iterative decoding and computer vision which involve… (More)

- Mohsen Bayati, Christian Borgs, Jennifer T. Chayes, Riccardo Zecchina
- SIAM J. Discrete Math.
- 2011

We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP) algorithm converges to the correct solution. We also show that when the LP relaxation has fractional solution then BP… (More)

We construct a deterministic fully polynomial time approximationscheme (FPTAS) for computing the total number of matchings in abounded degree graph. Additionally, for an arbitrary graph, weconstruct a deterministic algorithm for computing approximately thenumber of matchings within running time exp(O(√n log<sup>2</sup>n)),where <i>n</i> is the number… (More)

- Mohsen Bayati, Margot Gerritsen, David F. Gleich, Amin Saberi, Ying Wang
- 2009 Ninth IEEE International Conference on Data…
- 2009

We propose a new distributed algorithm for sparse variants of the network alignment problem, which occurs in a variety of data mining areas including systems biology, database matching, and computer vision. Our algorithm uses a belief propagation heuristic and provides near optimal solutions for this NP-hard combinatorial optimization problem. We show that… (More)

- Mohsen Bayati, David Gamarnik, Prasad Tetali
- STOC
- 2010

We establish the existence of free energy limits for several sparse random hypergraph models corresponding to certain combinatorial models on Erdos-Renyi (ER) graph G(N,c/N) and random r-regular graph G(N,r).
For a variety of models, including independent sets, MAX-CUT, Coloring and K-SAT, we prove that the free energy both at a positive and zero… (More)

- Mohsen Bayati, Marc Lelarge, Andrea Montanari
- ArXiv
- 2012

We consider a class of nonlinear mappings FA,N in R N indexed by symmetric random matrices A ∈ R with independent entries. Within spin glass theory, special cases of these mappings correspond to iterating the TAP equations and were studied by Erwin Bolthausen. Within information theory, they are known as ‘approximate message passing’ algorithms. We study… (More)

- Mohsen Bayati, Jeong Han Kim, Amin Saberi
- Algorithmica
- 2007

We present a nearly-linear time algorithm for counting and randomly generating simple graphs with a given degree sequence in a certain range. For degree sequence (d i ) i=1 n with maximum degree d max =O(m 1/4−τ ), our algorithm generates almost uniform random graphs with that degree sequence in time O(md max ) where $m=\frac{1}{2}\sum_{i}d_{i}$ is the… (More)