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This paper investigates two prominent probabilistic neural modeling paradigms: Bayesian Neural Networks (BNNs) and Mixture Density Networks (MDNs) for uncertainty-aware nonlinear regression. While BNNs incorporate epistemic uncertainty by…

Computation · Statistics 2025-10-30 Riddhi Pratim Ghosh , Ian Barnett

In the field of computational physics and material science, the efficient sampling of rare events occurring at atomic scale is crucial. It aids in understanding mechanisms behind a wide range of important phenomena, including protein…

Machine Learning · Computer Science 2024-01-17 Xinru Hua , Rasool Ahmad , Jose Blanchet , Wei Cai

Bayesian Inference offers principled tools to tackle many critical problems with modern neural networks such as poor calibration and generalization, and data inefficiency. However, scaling Bayesian inference to large architectures is…

Bayesian neural network (BNN) allows for uncertainty quantification in prediction, offering an advantage over regular neural networks that has not been explored in the differential privacy (DP) framework. We fill this important gap by…

Machine Learning · Computer Science 2023-02-21 Qiyiwen Zhang , Zhiqi Bu , Kan Chen , Qi Long

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…

Computational Engineering, Finance, and Science · Computer Science 2026-02-24 Giacomo Bottacini , Matteo Torzoni , Andrea Manzoni

The uncertainty of classification outcomes is of crucial importance for many safety critical applications including, for example, medical diagnostics. In such applications the uncertainty of classification can be reliably estimated within a…

Artificial Intelligence · Computer Science 2007-05-23 V. Schetinin , J. E. Fieldsend , D. Partridge , W. J. Krzanowski , R. M. Everson , T. C. Bailey , A. Hernandez

In this paper, we introduce BNN-DP, an efficient algorithmic framework for analysis of adversarial robustness of Bayesian Neural Networks (BNNs). Given a compact set of input points $T\subset \mathbb{R}^n$, BNN-DP computes lower and upper…

Machine Learning · Computer Science 2023-06-21 Steven Adams , Andrea Patane , Morteza Lahijanian , Luca Laurenti

Dropout has been witnessed with great success in training deep neural networks by independently zeroing out the outputs of neurons at random. It has also received a surge of interest for shallow learning, e.g., logistic regression. However,…

Machine Learning · Computer Science 2016-12-06 Zhe Li , Boqing Gong , Tianbao Yang

Bayesian neural networks (BNNs) have been an important framework in the study of uncertainty quantification. Deterministic variational inference, one of the inference methods, utilizes moment propagation to compute the predictive…

Machine Learning · Computer Science 2022-11-28 Yuki Hirayama , Sinya Takamaeda-Yamazaki

We study batch normalisation in the context of variational inference methods in Bayesian neural networks, such as mean-field or MC Dropout. We show that batch-normalisation does not affect the optimum of the evidence lower bound (ELBO).…

Machine Learning · Computer Science 2020-12-25 Jishnu Mukhoti , Puneet K. Dokania , Philip H. S. Torr , Yarin Gal

Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical…

Methodology · Statistics 2024-05-24 Yeseul Jeon , Won Chang , Seonghyun Jeong , Sanghoon Han , Jaewoo Park

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Machine Learning · Statistics 2020-02-27 Tim Pearce , Felix Leibfried , Alexandra Brintrup , Mohamed Zaki , Andy Neely

MC Dropout is a mainstream "free lunch" method in medical imaging for approximate Bayesian computations (ABC). Its appeal is to solve out-of-the-box the daunting task of ABC and uncertainty quantification in Neural Networks (NNs); to fall…

Meta-learning for few-shot learning allows a machine to leverage previously acquired knowledge as a prior, thus improving the performance on novel tasks with only small amounts of data. However, most mainstream models suffer from…

Machine Learning · Computer Science 2019-11-13 Yadan Luo , Zi Huang , Zheng Zhang , Ziwei Wang , Mahsa Baktashmotlagh , Yang Yang

Uncertainty approximation in text classification is an important area with applications in domain adaptation and interpretability. One of the most widely used uncertainty approximation methods is Monte Carlo (MC) Dropout, which is…

Machine Learning · Computer Science 2023-07-20 Andreas Nugaard Holm , Dustin Wright , Isabelle Augenstein

Modeling natural phenomena with artificial neural networks (ANNs) often provides highly accurate predictions. However, ANNs often suffer from over-parameterization, complicating interpretation and raising uncertainty issues. Bayesian neural…

Machine Learning · Statistics 2025-03-14 Eirik Høyheim , Lars Skaaret-Lund , Solve Sæbø , Aliaksandr Hubin

While state-of-the-art Deep Neural Network (DNN) models are considered to be robust to random perturbations, it was shown that these architectures are highly vulnerable to deliberately crafted perturbations, albeit being…

Machine Learning · Computer Science 2021-06-03 Omer Faruk Tuna , Ferhat Ozgur Catak , M. Taner Eskil

We propose an efficient way to output better calibrated uncertainty scores from neural networks. The Distilled Dropout Network (DDN) makes standard (non-Bayesian) neural networks more introspective by adding a new training loss which…

Computer Vision and Pattern Recognition · Computer Science 2018-09-28 Corina Gurau , Alex Bewley , Ingmar Posner

Deep convolutional neural networks (DCNNs) have dominated the recent developments in computer vision through making various record-breaking models. However, it is still a great challenge to achieve powerful DCNNs in resource-limited…

Computer Vision and Pattern Recognition · Computer Science 2019-08-20 Jiaxin Gu , Junhe Zhao , Xiaolong Jiang , Baochang Zhang , Jianzhuang Liu , Guodong Guo , Rongrong Ji

Uncertainty-aware semantic segmentation of the point clouds includes the predictive uncertainty estimation and the uncertainty-guided model optimization. One key challenge in the task is the efficiency of point-wise predictive distribution…

Computer Vision and Pattern Recognition · Computer Science 2022-01-20 Chao Qi , Jianqin Yin
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