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Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…

Survey data often arises from complex sampling designs, such as stratified or multistage sampling, with unequal inclusion probabilities. When sampling is informative, traditional inference methods yield biased estimators and poor coverage.…

Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or…

Neural networks are powerful predictive models, but they provide little insight into the nature of relationships between predictors and outcomes. Although numerous methods have been proposed to quantify the relative contributions of input…

Neural networks are powerful tools for cognitive modeling due to their flexibility and emergent properties. However, interpreting their learned representations remains challenging due to their sub-symbolic semantics. In this work, we…

One of the main problems of importance sampling in Bayesian networks is representation of the importance function, which should ideally be as close as possible to the posterior joint distribution. Typically, we represent an importance…

Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's…

This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping…

The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…

Many scientific models are composed of multiple discrete components, and scientists often make heuristic decisions about which components to include. Bayesian inference provides a mathematical framework for systematically selecting model…

Learning Bayesian networks is often cast as an optimization problem, where the computational task is to find a structure that maximizes a statistically motivated score. By and large, existing learning tools address this optimization problem…

Accurately estimating the informativeness of individual samples in a dataset is an important objective in deep learning, as it can guide sample selection, which can improve model efficiency and accuracy by removing redundant or potentially…

Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…

This study explores the potential of small language model(SLM) ensembles to achieve accuracy comparable to proprietary large language models (LLMs). We propose Ensemble Bayesian Inference (EBI), a novel approach that applies Bayesian…

Neural Networks (NNs) have provided state-of-the-art results for many challenging machine learning tasks such as detection, regression and classification across the domains of computer vision, speech recognition and natural language…

Neural responses in the cortex change over time both systematically, due to ongoing plasticity and learning, and seemingly randomly, due to various sources of noise and variability. Most previous work considered each of these processes,…

We examine the Bayes-consistency of a recently proposed 1-nearest-neighbor-based multiclass learning algorithm. This algorithm is derived from sample compression bounds and enjoys the statistical advantages of tight, fully empirical…

While perception tasks such as visual object recognition and text understanding play an important role in human intelligence, the subsequent tasks that involve inference, reasoning and planning require an even higher level of intelligence.…

Bayesian analysis plays a crucial role in estimating distribution of unknown parameters for given data and model. Due to the curse of dimensionality, it becomes difficult for high-dimensional problems, especially when multiple modes exist.…

A comprehensive artificial intelligence system needs to not only perceive the environment with different `senses' (e.g., seeing and hearing) but also infer the world's conditional (or even causal) relations and corresponding uncertainty.…