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Generative Bayesian Computation (GBC) methods are developed for Casual Inference. Generative methods are simulation-based methods that use a large training dataset to represent posterior distributions as a map (a.k.a. optimal transport) to…
The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing…
Laplace's method, a family of asymptotic methods used to approximate integrals, is presented as a potential candidate for the tool box of techniques used for knowledge acquisition and probabilistic inference in belief networks with…
Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these…
Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework…
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…
We introduce a new cluster-cumulant expansion (CCE) based on the fixed points of iterative belief propagation (IBP). This expansion is similar in spirit to the loop-series (LS) recently introduced in [1]. However, in contrast to the latter,…
Despite their widespread applications, Large Language Models (LLMs) often struggle to express uncertainty, posing a challenge for reliable deployment in high stakes and safety critical domains like clinical diagnostics. Existing standard…
Gaussian belief propagation (BP) has been widely used for distributed inference in large-scale networks such as the smart grid, sensor networks, and social networks, where local measurements/observations are scattered over a wide…
Approximate Bayesian computation (ABC) or likelihood-free inference algorithms are used to find approximations to posterior distributions without making explicit use of the likelihood function, depending instead on simulation of sample data…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…
With the wide-spread availability of complex relational data, semi-supervised node classification in graphs has become a central machine learning problem. Graph neural networks are a recent class of easy-to-train and accurate methods for…
In second-order uncertain Bayesian networks, the conditional probabilities are only known within distributions, i.e., probabilities over probabilities. The delta-method has been applied to extend exact first-order inference methods to…
Exact inference of marginals in probabilistic graphical models (PGM) is known to be intractable, necessitating the use of approximate methods. Most of the existing variational techniques perform iterative message passing in loopy graphs…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
Inference for belief networks using Gibbs sampling produces a distribution for unobserved variables that differs from the correct distribution by a (usually) unknown error, since convergence to the right distribution occurs only…
In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP algorithm in a…
Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework…
Inference for probabilistic graphical models is still very much a practical challenge in large domains. The commonly used and effective belief propagation (BP) algorithm and its generalizations often do not converge when applied to hard,…
The generalized linear mixed model (GLMM) is widely used for analyzing correlated data, particularly in large-scale biomedical and social science applications. Scalable Bayesian inference for GLMMs is challenging because the marginal…