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Belief propagation (BP) is a message-passing heuristic for statistical inference in graphical models such as Bayesian networks and Markov random fields. BP is used to compute marginal distributions or maximum likelihood assignments and has…
Expectation Propagation (EP) is a widely used iterative message-passing algorithm that decomposes a global inference problem into multiple local ones. It approximates marginal distributions as ``beliefs'' using intermediate functions called…
Non-Gaussian likelihoods, ubiquitous throughout cosmology, are a direct consequence of nonlinearities in the physical model. Their treatment requires Monte-Carlo Markov-chain or more advanced sampling methods for the determination of…
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message…
We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within…
We consider a partially asymmetric exclusion process (PASEP) on a finite number of sites with open and directed boundary conditions. Its partition function was calculated by Blythe, Evans, Colaiori, and Essler. It is known to be a…
We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the…
We consider the general problem of finding the minimum weight $\bm$-matching on arbitrary graphs. We prove that, whenever the linear programming (LP) relaxation of the problem has no fractional solutions, then the belief propagation (BP)…
We consider the problem of estimating the missing mass, partition function or evidence and its probability distribution in the case that for each sample point in the discrete sample space its (unnormalized) probability mass is revealed.…
Belief propagation (BP) algorithm is a widely used message-passing method for inference in graphical models. BP on loop-free graphs converges in linear time. But for graphs with loops, BP's performance is uncertain, and the understanding of…
Belief Propagation (BP) is one of the most popular methods for inference in probabilistic graphical models. BP is guaranteed to return the correct answer for tree structures, but can be incorrect or non-convergent for loopy graphical…
We investigate dynamics of an inference algorithm termed the belief propagation (BP) when employed in spin glass (SG) models and show that its macroscopic behaviors can be traced by recursive updates of certain auxiliary field distributions…
In many experimental designs -- split-plots, blocked or nested layouts, fractional factorials, and studies with missing or unequal replication -- standard ANOVA procedures no longer tell us exactly how many independent pieces of information…
Belief propagation is a powerful tool in statistical physics, machine learning, and modern coding theory. As a decoding method, it is ubiquitous in classical error correction and has also been applied to stabilizer-based quantum error…
We investigate the behavior of the rare fluctuations of the free energy in the p-spin spherical model, evaluating the corresponding rate function via the G\"artner-Ellis theorem. This approach requires the knowledge of the analytic…
The "marginal" distributions for measurable coordinate and spin projection is introduced. Then, the analog of the Pauli equation for spin-1/2 particle is obtained for such probability distributions instead of the usual wave functions. That…
An "element-free" probability distribution is what remains of a probability distribution after we forget the elements to which the probabilities were assigned. These objects naturally arise in Bayesian statistics, in situations where…
Recent years have seen a growing interest in the use of belief propagation - an algorithm originally introduced for performing statistical inference on graphical models - for approximate, but highly efficient, tensor network contraction.…
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…
Variational message passing (VMP), belief propagation (BP) and expectation propagation (EP) have found their wide applications in complex statistical signal processing problems. In addition to viewing them as a class of algorithms operating…