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Quantile regression is often used when a comprehensive relationship between a response variable and one or more explanatory variables is desired. The traditional frequentists' approach to quantile regression has been well developed around…

Statistics Theory · Mathematics 2015-06-03 Yang Feng , Yuguo Chen , Xuming He

As autonomous systems increasingly rely on Deep Neural Networks (DNN) to implement the navigation pipeline functions, uncertainty estimation methods have become paramount for estimating confidence in DNN predictions. Bayesian Deep Learning…

Robotics · Computer Science 2023-01-16 Fabio Arnez , Huascar Espinoza , Ansgar Radermacher , François Terrier

Bayesian methods have shown success in deep learning applications. For example, in predictive tasks, Bayesian neural networks leverage Bayesian reasoning of model uncertainty to improve the reliability and uncertainty awareness of deep…

Machine Learning · Computer Science 2025-10-21 Wenlong Chen , Bolian Li , Ruqi Zhang , Yingzhen Li

We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…

Methodology · Statistics 2025-09-25 Lu Zhang , Wenpin Tang , Sudipto Banerjee

We study probit regression from a Bayesian perspective and give an alternative form for the posterior distribution when the prior distribution for the regression parameters is the uniform distribution. This new form allows simple Monte…

Methodology · Statistics 2012-03-15 Yuzo Maruyama , William E. Strawderman

In recent years, inconsistency in Bayesian deep learning has attracted significant attention. Tempered or generalized posterior distributions are frequently employed as direct and effective solutions. Nonetheless, the underlying mechanisms…

Machine Learning · Computer Science 2025-09-23 Yinsong Chen , Samson S. Yu , Zhong Li , Chee Peng Lim

The Bayesian Mallows model is a flexible tool for analyzing data in the form of complete or partial rankings, and transitive or intransitive pairwise preferences. In many potential applications of preference learning, data arrive…

Computation · Statistics 2025-11-26 Øystein Sørensen , Anja Stein , Waldir Leoncio Netto , David S. Leslie

The fairness of a deep neural network is strongly affected by dataset bias and spurious correlations, both of which are usually present in modern feature-rich and complex visual datasets. Due to the difficulty and variability of the task,…

Computer Vision and Pattern Recognition · Computer Science 2024-02-28 Rebecca S Stone , Nishant Ravikumar , Andrew J Bulpitt , David C Hogg

Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior…

Machine Learning · Statistics 2019-08-27 Edwin Fong , Simon Lyddon , Chris Holmes

Recent work has shown that the prior over functions induced by a deep Bayesian neural network (BNN) behaves as a Gaussian process (GP) as the width of all layers becomes large. However, many BNN applications are concerned with the BNN…

Machine Learning · Statistics 2020-11-30 Jiri Hron , Yasaman Bahri , Roman Novak , Jeffrey Pennington , Jascha Sohl-Dickstein

High-dimensional linear models have been widely studied, but the developments in high-dimensional generalized linear models, or GLMs, have been slower. In this paper, we propose an empirical or data-driven prior leading to an empirical…

Statistics Theory · Mathematics 2025-07-09 Yiqi Tang , Ryan Martin

We recapitulate the Bayesian formulation of neural network based classifiers and show that, while sampling from the posterior does indeed lead to better generalisation than is obtained by standard optimisation of the cost function, even…

Machine Learning · Statistics 2019-04-09 Robert J. N. Baldock , Nicola Marzari

Modern challenges of robustness, fairness, and decision-making in machine learning have led to the formulation of multi-distribution learning (MDL) frameworks in which a predictor is optimized across multiple distributions. We study the…

Machine Learning · Computer Science 2024-12-19 Rajeev Verma , Volker Fischer , Eric Nalisnick

This article presents a Bayesian inferential method where the likelihood for a model is unknown but where data can easily be simulated from the model. We discretize simulated (continuous) data to estimate the implicit likelihood in a…

Model Compression has drawn much attention within the deep learning community recently. Compressing a dense neural network offers many advantages including lower computation cost, deployability to devices of limited storage and memories,…

Machine Learning · Computer Science 2024-11-04 Diptarka Saha , Zihe Liu , Feng Liang

The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…

Logic in Computer Science · Computer Science 2015-07-01 Johannes Borgström , Andrew D Gordon , Michael Greenberg , James Margetson , Jurgen Van Gael

We investigate the use of normalizing flow (NF) models as flexible priors in Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling for iterative Bayesian calibration. Trained on posteriors from previous analyses, these models can…

Nuclear Theory · Physics 2026-04-02 Hendrik Roch , Chun Shen

Unsupervised deep-learning (DL) models were recently proposed for deformable image registration tasks. In such models, a neural-network is trained to predict the best deformation field by minimizing some dissimilarity function between the…

Computer Vision and Pattern Recognition · Computer Science 2020-08-11 Samah Khawaled , Moti Freiman

Epigenetic observations are represented by the total number of reads from a given pool of cells and the number of methylated reads, making it reasonable to model this data by a binomial distribution. There are numerous factors that can…

Applications · Statistics 2020-04-29 Aliaksandr Hubin , Geir O Storvik , Paul E Grini , Melinka A Butenko

Mechanistic models of single-neuron dynamics have been extensively studied in computational neuroscience. However, identifying which models can quantitatively reproduce empirically measured data has been challenging. We propose to overcome…

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