相关论文: Message passing in random satisfiability problems
We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same…
We study the set of solutions of random k-satisfiability formulae through the cavity method. It is known that, for an interval of the clause-to-variables ratio, this decomposes into an exponential number of pure states (clusters). We refine…
We study the problem of satisfiability of randomly chosen clauses, each with K Boolean variables. Using the cavity method at zero temperature, we find the phase diagram for the K=3 case. We show the existence of an intermediate phase in the…
Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or…
A method to approximately close the dynamic cavity equations for synchronous reversible dynamics on a locally tree-like topology is presented. The method builds on $(a)$ a graph expansion to eliminate loops from the normalizations of each…
We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly…
Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin…
An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…
The solution space of a K-satisfiability (K-SAT) formula is a collection of solution clusters, each of which contains all the solutions that are mutually reachable through a sequence of single-spin flips. Knowledge of the statistical…
We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We…
In this letter, we introduce a novel message-passing algorithm for a class of problems which can be mathematically understood as estimating volume-related properties of random polytopes. Unlike the usual approach consisting in approximating…
Over the last decade or so, Approximate Message Passing (AMP) algorithms have become extremely popular in various structured high-dimensional statistical problems. The fact that the origins of these techniques can be traced back to notions…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
We use the cavity method from statistical physics for analyzing the transient and stationary dynamics of a minority game that is played by agents performing market arbitrage. On the level of linear response the method allows to include the…
We study local search algorithms to solve instances of the random $k$-satisfiabi lity problem, equivalent to finding (if they exist) zero-energy ground states of statistical models with disorder on random hypergraphs. It is well known that…
Penalized regression methods aim to retrieve reliable predictors among a large set of putative ones from a limited amount of measurements. In particular, penalized regression with singular penalty functions is important for sparse…
A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to…
An improved inference method for densely connected systems is presented. The approach is based on passing condensed messages between variables, representing macroscopic averages of microscopic messages. We extend previous work that showed…
We study hard constraint satisfaction problems with a decimation approach based on message passing algorithms. Decimation induces a renormalization flow in the space of problems, and we exploit the fact that this flow transforms some of the…
Survey Propagation is an algorithm designed for solving typical instances of random constraint satisfiability problems. It has been successfully tested on random 3-SAT and random $G(n,\frac{c}{n})$ graph 3-coloring, in the hard region of…