Related papers: Simplifying Generalized Belief Propagation on Redu…

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…

There is an increasing interest in scaling tensor network methods through belief propagation (BP), as well as increasing the accuracy of BP through tensor network methods. We develop a unification framework that takes an arbitrary graphical…

Learning general latent-variable probabilistic graphical models is a key theoretical challenge in machine learning and artificial intelligence. All previous methods, including the EM algorithm and the spectral algorithms, face severe…

Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice,…

Belief propagation is known to perform extremely well in many practical statistical inference and learning problems using graphical models, even in the presence of multiple loops. The iterative use of belief propagation algorithm on loopy…

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 this paper, we first propose an unconditionally stable implicit difference scheme for solving generalized time-space fractional diffusion equations (GTSFDEs) with variable coefficients. The numerical scheme utilizes the $L1$-type formula…

Variational inference algorithms such as belief propagation have had tremendous impact on our ability to learn and use graphical models, and give many insights for developing or understanding exact and approximate inference. However,…

We first present an empirical study of the Belief Propagation (BP) algorithm, when run on the random field Ising model defined on random regular graphs in the zero temperature limit. We introduce the notion of maximal solutions for the BP…

Recently, M. Chertkov and V.Y. Chernyak derived an exact expression for the partition sum (normalization constant) corresponding to a graphical model, which is an expansion around the Belief Propagation solution. By adding correction terms…

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…

Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…

The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…

Belief Propagation has been widely used for marginal inference, however it is slow on problems with large-domain variables and high-order factors. Previous work provides useful approximations to facilitate inference on such models, but…

Graph Neural Networks (GNNs) have received increasing attention due to their ability to learn from graph-structured data. However, their predictions are often not interpretable. Post-hoc instance-level explanation methods have been proposed…

The max-product {belief propagation} (BP) is a popular message-passing heuristic for approximating a maximum-a-posteriori (MAP) assignment in a joint distribution represented by a graphical model (GM). In the past years, it has been shown…

We present an exact method of greatly speeding up belief propagation (BP) for a wide variety of potential functions in pairwise MRFs and other graphical models. Specifically, our technique applies whenever the pairwise potentials have been…

Recently there has been an increasing interest in the multivariate Gaussian process (MGP) which extends the Gaussian process (GP) to deal with multiple outputs. One approach to construct the MGP and account for non-trivial commonalities…

The multivariate adaptive regression spline (MARS) approach of Friedman (1991) and its Bayesian counterpart (Francom et al. 2018) are effective approaches for the emulation of computer models. The traditional assumption of Gaussian errors…

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…