Related papers: Belief Propagation on the random $k$-SAT model
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 introduce and study the problem of posterior inference on tree-structured graphical models in the presence of a malicious adversary who can corrupt some observed nodes. In the well-studied broadcasting on trees model, corresponding to…
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…
A non-Hermitian region connected to semi-infinite Hermitian lattices acts either as a source or as a sink and the probability current is not conserved in a scattering typically. Even a $\mathcal{P}\mathcal{T}$-symmetric region that contains…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…
Belief Propagation (BP) is a popular, distributed heuristic for performing MAP computations in Graphical Models. BP can be interpreted, from a variational perspective, as minimizing the Bethe Free Energy (BFE). BP can also be used to solve…
We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally…
We study several bayesian inference problems for irreversible stochastic epidemic models on networks from a statistical physics viewpoint. We derive equations which allow to accurately compute the posterior distribution of the time…
We propose a hybrid message passing method for distributed cooperative localization and tracking of mobile agents. Belief propagation and mean field message passing are employed for, respectively, the motion-related and measurement-related…
We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the…
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. Its worst-case hardness lies at the core of computational complexity theory, for example in the form of NP-hardness and the (Strong) Exponential…
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…
A Monte-Carlo algorithm for discrete statistical models that combines the full power of the Belief Propagation algorithm with the advantages of a detailed-balanced heat bath approach is presented. A sub-tree inside the factor graph is first…
We prove the existence of full replica symmetry breaking (FRSB) for the Sherrington-Kirkpatrick (SK) model at low temperature. More specifically, we prove that slightly beyond the critical temperature, the Parisi measure for the SK model is…
Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference;…
We study the performance of different message passing algorithms in the two dimensional Edwards Anderson model. We show that the standard Belief Propagation (BP) algorithm converges only at high temperature to a paramagnetic solution. Then,…
We consider the estimation of an i.i.d.\ random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message…
Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes, yet existing…
In Bayesian networks, exact belief propagation is achieved through message passing algorithms. These algorithms (ex: inward and outward) provide only a recursive definition of the corresponding messages. In contrast, when working on hidden…
We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…