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Belief propagation is an algorithm that is known from statistical physics and computer science. It provides an efficient way of calculating marginals that involve large sums of products which are efficiently rearranged into nested products…

Identifying important features linked to a response variable is a fundamental task in various scientific domains. This article explores statistical inference for simulated Markov random fields in high-dimensional settings. We introduce a…

The Markov chain random field (MCRF) model/theory provides a non-linear spatial Bayesian updating solution at the neighborhood nearest data level for simulating categorical spatial variables. In the MCRF solution, the spatial dependencies…

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…

In this paper we derive the equations for Loop Corrected Belief Propagation on a continuous variable Gaussian model. Using the exactness of the averages for belief propagation for Gaussian models, a different way of obtaining the…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

As a nonparametric statistical inference approach, empirical likelihood has been found very useful in numerous occasions. However, it encounters serious computational challenges when applied directly to the modern massive dataset. This…

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…

Loopy belief propagation performs approximate inference on graphical models with loops. One might hope to compensate for the approximation by adjusting model parameters. Learning algorithms for this purpose have been explored previously,…

We consider the problem of approximate Bayesian inference in log-supermodular models. These models encompass regular pairwise MRFs with binary variables, but allow to capture high-order interactions, which are intractable for existing…

We present a major improvement to the incremental pruning algorithm for solving partially observable Markov decision processes. Our technique targets the cross-sum step of the dynamic programming (DP) update, a key source of complexity in…

Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple…

We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…

Searching recurrent patterns in complex systems with high-dimensional phase spaces is an important task in diverse fields. In the current work, an improved scheme is proposed to accelerate the recently designed variational approach for…

We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…

The application of machine learning models can be significantly impeded by the occurrence of distributional shifts, as the assumption of homogeneity between the population of training and testing samples in machine learning and statistics…

Gaussian belief propagation (GBP) is a recursive computation method that is widely used in inference for computing marginal distributions efficiently. Depending on how the factorization of the underlying joint Gaussian distribution is…

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…

Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…

This paper addresses a key limitation in existing counterfactual inference methods for Markov Decision Processes (MDPs). Current approaches assume a specific causal model to make counterfactuals identifiable. However, there are usually many…