Related papers: Belief propagation with multipoint correlations an…
We introduce a differential complex of local observables given a decomposition of a global set of random variables into subsets. Its boundary operator allows us to define a transport equation equivalent to Belief Propagation. This…
Belief propagation (BP) is a message-passing method for solving probabilistic graphical models. It is very successful in treating disordered models (such as spin glasses) on random graphs. On the other hand, finite-dimensional lattice…
Many datasets give partial information about an ordering or ranking by indicating which team won a game, which item a user prefers, or who infected whom. We define a continuous spin system whose Gibbs distribution is the posterior…
Belief propagation is a well-studied algorithm for approximating local marginals of multivariate probability distribution over complex networks, while tensor network states are powerful tools for quantum and classical many-body problems.…
We develop a transfer matrix method to compute exactly the spin-spin correlation functions of Bethe lattice spin models in the external magnetic field h and for any temperature T. We first compute the correlation function for the most…
A number of problems in statistical physics and computer science can be expressed as the computation of marginal probabilities over a Markov random field. Belief propagation, an iterative message-passing algorithm, computes exactly such…
We present a large deviations theory of the spin-spin correlation functions in the Random Field Ising Model on the Bethe lattice, both at finite and zero temperature. Rare events of atypically correlated variables are particularly important…
In graphical models, factor graphs, and more generally energy-based models, the interactions between variables are encoded by a graph, a hypergraph, or, in the most general case, a partially ordered set (poset). Inference on such…
We present a systematic small-correlation expansion to solve the inverse Ising problem: find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in…
Belief propagation is a fundamental message-passing algorithm for numerous applications in machine learning. It is known that belief propagation algorithm is exact on tree graphs. However, belief propagation is run on loopy graphs in most…
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 apply the Bethe-Peierls approximation to the problem of the inverse Ising model and show how the linear response relation leads to a simple method to reconstruct couplings and fields of the Ising model. This reconstruction is exact on…
Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference,…
Using the algebraic Bethe ansatz method, and the solution of the quantum inverse scattering problem for local spins, we obtain multiple integral representations of the $n$-point correlation functions of the XXZ Heisenberg spin-$1 \over 2$…
In this thesis, new generalizations of the Bethe approximation and new understanding of the replica method are proposed. The Bethe approximation is an efficient approximation for graphical models, which gives an asymptotically accurate…
An improved unified formulation based on the effective field theory is introduced for a spin-1 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the…
An improved unified formulation based on the effective field theory is introduced for a spin-1/2 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the…
The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…
Belief propagation -- a powerful heuristic method to solve inference problems involving a large number of random variables -- was recently generalized to quantum theory. Like its classical counterpart, this algorithm is exact on trees when…
Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces…