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A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…
Message passing algorithms have proved surprisingly successful in solving hard constraint satisfaction problems on sparse random graphs. In such applications, variables are fixed sequentially to satisfy the constraints. Message passing is…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
We study asymptotic properties of expectation propagation (EP) -- a method for approximate inference originally developed in the field of machine learning. Applied to generalized linear models, EP iteratively computes a multivariate…
Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an…
Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…
In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…
Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that…
Constructing a minimal vertex cover of a graph can be seen as a prototype for a combinatorial optimization problem under hard constraints. In this paper, we develop and analyze message passing techniques, namely warning and survey…
We consider the problem of calculating learning curves (i.e., average generalization performance) of Gaussian processes used for regression. On the basis of a simple expression for the generalization error, in terms of the eigenvalue…
We propose an approach to do learning in Gaussian factor graphs. We treat all relevant quantities (inputs, outputs, parameters, latents) as random variables in a graphical model, and view both training and prediction as inference problems…
Gaussian belief propagation (BP) has been widely used for distributed estimation in large-scale networks such as the smart grid, communication networks, and social networks, where local measurements/observations are scattered over a wide…
Belief Propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals. The resulting approximations are equivalent to the Bethe-Peierls…
Gaussian Belief Propagation (BP) algorithm is one of the most important distributed algorithms in signal processing and statistical learning involving Markov networks. It is well known that the algorithm correctly computes marginal density…
We describe a continuous variable error correction protocol that can correct the Gaussian noise induced by linear loss on Gaussian states. The protocol can be implemented using linear optics and photon counting. We explore the theoretical…
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,…
The holographic transformation, belief propagation and loop calculus are generalized to problems in generalized probabilistic theories including quantum mechanics. In this work, the partition function of classical factor graph is…
Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of…
Gaussian belief propagation (GaBP) is an iterative algorithm for computing the mean of a multivariate Gaussian distribution, or equivalently, the minimum of a multivariate positive definite quadratic function. Sufficient conditions, such as…
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…