Related papers: Message passing in random satisfiability problems
Most optimization problems in applied sciences realistically involve uncertainty in the parameters defining the cost function, of which only statistical information is known beforehand. In a recent work we introduced a message passing…
A new field of research is rapidly expanding at the crossroad between statistical physics, information theory and combinatorial optimization. In particular, the use of cutting edge statistical physics concepts and methods allow one to solve…
We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models. This method is developed in…
We study the satisfiability of randomly generated formulas formed by $M$ clauses of exactly $K$ literals over $N$ Boolean variables. For a given value of $N$ the problem is known to be most difficult with $\alpha=M/N$ close to the…
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is…
Message passing algorithms, whose iterative nature captures well complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages, provide a powerful toolkit in…
This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…
Networks and network computations have become a primary mathematical tool for analyzing the structure of many kinds of complex systems, ranging from the Internet and transportation networks to biochemical interactions and social networks. A…
In this three-sections lecture cavity method is introduced as heuristic framework from a Physics perspective to solve probabilistic graphical models and it is presented both at the replica symmetric (RS) and 1-step replica symmetry breaking…
The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the…
In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the…
We study the susceptibility propagation, a message-passing algorithm to compute correlation functions. It is applied to constraint satisfaction problems and its accuracy is examined. As a heuristic method to find a satisfying assignment, we…
Constructing a minimal vertex cover of a graph can be seen as a prototype for a combinatorial optimization problem under hard constraints. In this paper, we develop and analyze message passing techniques, namely warning and survey…
Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in…
Much of the recent work on random constraint satisfaction problems has been inspired by ingenious but non-rigorous approaches from physics. The physics predictions typically come in the form of distributional fixed point problems that are…
Message-passing methods provide a powerful approach for calculating the expected size of cascades either on random networks (e.g., drawn from a configuration-model ensemble or its generalizations) asymptotically as the number $N$ of nodes…
In this paper we derive the equations for Loop Corrected Belief Propagation on a continuous variable Gaussian model. Using the exactness of the averages for belief propagation for Gaussian models, a different way of obtaining the…
Resampling techniques are widely used in statistical inference and ensemble learning, in which estimators' statistical properties are essential. However, existing methods are computationally demanding, because repetitions of…
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…
In this work we introduce a novel weighted message-passing algorithm based on the cavity method to estimate volume-related properties of random polytopes, properties which are relevant in various research fields ranging from metabolic…