Related papers: Bethe states of random factor graphs
Consider a discrete locally finite subset $\Gamma$ of $R^d$ and the complete graph $(\Gamma,E)$, with vertices $\Gamma$ and edges $E$. We consider Gibbs measures on the set of sub-graphs with vertices $\Gamma$ and edges $E'\subset E$. The…
Quantum systems in thermal equilibrium are described using Gibbs states. The correlations in such states determine how difficult it is to describe or simulate them. In this article, we show that if the Gibbs state of a quantum system…
We present a novel inference algorithm for arbitrary, binary, undirected graphs. Unlike loopy belief propagation, which iterates fixed point equations, we directly descend on the Bethe free energy. The algorithm consists of two phases,…
We show that under a low complexity condition on the gradient of a Hamiltonian, Gibbs distributions on the Boolean hypercube are approximate mixtures of product measures whose probability vectors are critical points of an associated…
In the study of random structures we often face a trade-off between realism and tractability, the latter typically enabled by assuming some form of independence. In this work we initiate an effort to bridge this gap by developing tools that…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
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…
We study criteria which ensure that Gibbs states (often also called generalized vacuum states) on distance-regular graphs are positive. Our main criterion assumes that the graph can be embedded into a growing family of distance-regular…
We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
According to Popescu's recent analysis [Phys. Rev. Lett. {\bf72}, 797 (1994)], {\it nonideal} measurements, rather than ideal ones, may be more sensitive to reveal nonlocal correlations between distant parts of composite quantum systems.…
A simple picture for the spectrum of the one-dimensional Hubbard model is presented using a classification of the eigenstates based on an intuitive bound-state Bethe-Ansatz approach. This approach allows us to prove a "string hypothesis"…
We derive two related novel bounds on single-variable marginal probability distributions in factor graphs with discrete variables. The first method propagates bounds over a subtree of the factor graph rooted in the variable, and the second…
We derive new explicit bounds for the total variation distance between two convolution products of $n$ probability distributions, one of which having identical convolution factors. Approximations by finite signed measures of arbitrary order…
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…
Belief Propagation (BP) is a powerful algorithm for distributed inference in probabilistic graphical models, however it quickly becomes infeasible for practical compute and memory budgets. Many efficient, non-parametric forms of BP have…
The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each…
In a smooth semiparametric model, the marginal posterior distribution of the finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of frequentist's efficient estimators. This is…
This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…