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We study coalition structure generation (CSG) when coalition values are not given but must be learned from episodic observations. We model each episode as a sparse linear regression problem, where the realised payoff \(Y_t\) is a noisy…

We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Polya-Gamma distributions, which are constructed in detail. A variety of examples are…

Exact inference in Bayesian networks is intractable and has an exponential dependence on the size of the largest clique in the corresponding clique tree (CT), necessitating approximations. Factor based methods to bound clique sizes are more…

Numerical simulations are crucial for modeling complex systems, but calibrating them becomes challenging when data are noisy or incomplete and likelihood evaluations are computationally expensive. Bayesian calibration offers an interesting…

Gaussian processes (GPs) provide a principled Bayesian framework for uncertainty estimation, but their computational complexity severely limits scalability to large datasets. We propose SIKA-GP, which accelerates GP inference using sparse…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

Divide-and-conquer based methods for Bayesian inference provide a general approach for tractable posterior inference when the sample size is large. These methods divide the data into smaller subsets, sample from the posterior distribution…

The computational efficiency of approximate Bayesian computation (ABC) has been improved by using surrogate models such as Gaussian processes (GP). In one such promising framework the discrepancy between the simulated and observed data is…

Many of the causal discovery methods rely on the faithfulness assumption to guarantee asymptotic correctness. However, the assumption can be approximately violated in many ways, leading to sub-optimal solutions. Although there is a line of…

Approximate Bayesian computation (ABC) methods are used to approximate posterior distributions using simulation rather than likelihood calculations. We introduce Gaussian process (GP) accelerated ABC, which we show can significantly reduce…

We propose SWA-Gaussian (SWAG), a simple, scalable, and general purpose approach for uncertainty representation and calibration in deep learning. Stochastic Weight Averaging (SWA), which computes the first moment of stochastic gradient…

Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…

Bayesian methods provide an elegant framework for estimating parameter posteriors and quantification of uncertainty associated with probabilistic models. However, they often suffer from slow inference times. To address this challenge,…

A wide range of optimization problems arising in machine learning can be solved by gradient descent algorithms, and a central question in this area is how to efficiently compress a large-scale dataset so as to reduce the computational…

Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a…

Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations…

The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm, where a quantum computer implements a variational ansatz consisting of $p$ layers of alternating unitary operators and a classical computer is used to…

We propose a group information geometry approach (GIGA) for ultra-massive multiple-input multiple-output (MIMO) signal detection. The signal detection task is framed as computing the approximate marginals of the a posteriori distribution of…