Related papers: High-temperature Expansions and Message Passing Al…
We show that the hierarchical model at finite volume has a symmetry group which can be decomposed into rotations and translations as the familiar Poincar\'e groups. Using these symmetries, we show that the intricate sums appearing in the…
Motivated by recent progress in using restricted Boltzmann machines as preprocessing algorithms for deep neural network, we revisit the mean-field equations (belief-propagation and TAP equations) in the best understood such machine, namely…
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,…
The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
We consider a broad class of Approximate Message Passing (AMP) algorithms defined as a Lipschitzian functional iteration in terms of an $n\times n$ random symmetric matrix $A$. We establish universality in noise for this AMP in the…
The high temperature expansion is an analytical tool to study critical phenomena in statistical mechanics. We apply this method to 3d effective theories of Polyakov loops, which have been derived from 4d lattice Yang-Mills by means of…
The thermal equilibrium properties of physical systems can be described using Gibbs states. It is therefore of great interest to know when such states allow for an easy description. In particular, this is the case if correlations between…
This paper studies the convergence rate of a message-passing distributed algorithm for solving a large-scale linear system. This problem is generalised from the celebrated Gaussian Belief Propagation (BP) problem for statistical learning…
The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's…
In this paper, we suppose a possible extension of Gibbs ensemble theory so that it can provide a reasonable description to phase transitions and spontaneous symmetry breaking. The extension is founded on three hypotheses, and can be…
In this paper we treat both forms of probabilistic inference, estimating marginal probabilities of the joint distribution and finding the most probable assignment, through a unified message-passing algorithm architecture. We generalize the…
We formulate the high temperature expansion in supersymmetric matrix quantum mechanics with 4, 8 and 16 supercharges. The models can be obtained by dimensionally reducing N=1 U(N) super Yang-Mills theory in D=4,6,10 to 1 dimension,…
This paper presents a unified framework to understand the dynamics of message-passing algorithms in compressed sensing. State evolution is rigorously analyzed for a general error model that contains the error model of approximate…
The optimized linear $\delta$-expansion is applied to the $\lambda \phi^4$ theory at high temperature. Using the imaginary time formalism the thermal mass is evaluated perturbatively up to order $\delta^2$. A variational procedure…
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…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
The maximum entropy principle (MEP) is one of the most prominent methods to investigate and model complex systems. Despite its popularity, the standard form of the MEP can only generate Boltzmann-Gibbs distributions, which are ill-suited…
We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…
High-dimensional signal recovery of standard linear regression is a key challenge in many engineering fields, such as, communications, compressed sensing, and image processing. The approximate message passing (AMP) algorithm proposed by…