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In this paper, we present a guide to the foundations of learning Dynamic Bayesian Networks (DBNs) from data in the form of multiple samples of trajectories for some length of time. We present the formalism for a generic as well as a set of…

Machine Learning · Computer Science 2024-09-02 Vyacheslav Kungurtsev , Fadwa Idlahcen , Petr Rysavy , Pavel Rytir , Ales Wodecki

We propose a novel deep learning tool in order to study the evolution of dark energy models. The aim is to combine two architectures: the Recurrent Neural Networks (RNN) and the Bayesian Neural Networks (BNN), we named this full network as…

Cosmology and Nongalactic Astrophysics · Physics 2020-03-18 Celia Escamilla-Rivera , Maryi Alejandra Carvajal Quintero , S. Capozziello

Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded…

Machine Learning · Statistics 2016-10-05 Yarin Gal , Zoubin Ghahramani

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…

Machine Learning · Statistics 2026-04-21 Ethan Goan , Clinton Fookes

We describe Bayesian Layers, a module designed for fast experimentation with neural network uncertainty. It extends neural network libraries with drop-in replacements for common layers. This enables composition via a unified abstraction…

Machine Learning · Computer Science 2019-03-07 Dustin Tran , Michael W. Dusenberry , Mark van der Wilk , Danijar Hafner

Although deep neural networks have demonstrated significant success due to their powerful expressiveness, most models struggle to meet practical requirements for uncertainty estimation. Concurrently, the entangled nature of deep neural…

Machine Learning · Computer Science 2025-05-29 Xinyue Hu , Zhibin Duan , Bo Chen , Mingyuan Zhou

Deep neural networks(NNs) have achieved impressive performance, often exceed human performance on many computer vision tasks. However, one of the most challenging issues that still remains is that NNs are overconfident in their predictions,…

Machine Learning · Computer Science 2019-12-30 Chanwoo Park , Jae Myung Kim , Seok Hyeon Ha , Jungwoo Lee

Modern neural networks have found to be miscalibrated in terms of confidence calibration, i.e., their predicted confidence scores do not reflect the observed accuracy or precision. Recent work has introduced methods for post-hoc confidence…

Computer Vision and Pattern Recognition · Computer Science 2021-09-22 Fabian Küppers , Jan Kronenberger , Jonas Schneider , Anselm Haselhoff

We present two methods to reduce the complexity of Bayesian network (BN) classifiers. First, we introduce quantization-aware training using the straight-through gradient estimator to quantize the parameters of BNs to few bits. Second, we…

Machine Learning · Computer Science 2021-09-23 Wolfgang Roth , Günther Schindler , Holger Fröning , Franz Pernkopf

To better understand the theoretical behavior of large neural networks, several works have analyzed the case where a network's width tends to infinity. In this regime, the effect of random initialization and the process of training a neural…

Machine Learning · Computer Science 2022-01-14 Florian Juengermann , Maxime Laasri , Marius Merkle

Measuring the structural parameters (size, total brightness, light concentration, etc.) of galaxies is a significant first step towards a quantitative description of different galaxy populations. In this work, we demonstrate that a Bayesian…

Instrumentation and Methods for Astrophysics · Physics 2022-07-08 Dimitrios Tanoglidis , Aleksandra Ćiprijanović , Alex Drlica-Wagner

Bayesian neural networks (BNN) and deep ensembles are principled approaches to estimate the predictive uncertainty of a deep learning model. However their practicality in real-time, industrial-scale applications are limited due to their…

Machine Learning · Computer Science 2020-10-27 Jeremiah Zhe Liu , Zi Lin , Shreyas Padhy , Dustin Tran , Tania Bedrax-Weiss , Balaji Lakshminarayanan

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

Machine Learning · Statistics 2020-01-16 Ali Siahkoohi , Gabrio Rizzuti , Felix J. Herrmann

Quantifying the uncertainty in the output of a neural network is essential for deployment in scientific or engineering applications where decisions must be made under limited or noisy data. Bayesian neural networks (BNNs) provide a…

Machine Learning · Statistics 2026-03-10 Alex Alberts , Ilias Bilionis

In this work, we demonstrate the Empirical Bayes approach to learning a Dynamic Bayesian Network. By starting with several point estimates of structure and weights, we can use a data-driven prior to subsequently obtain a model to quantify…

Machine Learning · Computer Science 2024-07-02 Vyacheslav Kungurtsev , Apaar , Aarya Khandelwal , Parth Sandeep Rastogi , Bapi Chatterjee , Jakub Mareček

Convolutional neural network (CNN) has achieved unprecedented success in image super-resolution tasks in recent years. However, the network's performance depends on the distribution of the training sets and degrades on out-of-distribution…

Computer Vision and Pattern Recognition · Computer Science 2021-05-20 Aupendu Kar , Prabir Kumar Biswas

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

Bayesian learning of model parameters in neural networks is important in scenarios where estimates with well-calibrated uncertainty are important. In this paper, we propose Bayesian quantized networks (BQNs), quantized neural networks…

Machine Learning · Computer Science 2019-12-09 Jiahao Su , Milan Cvitkovic , Furong Huang

Continuous-time Bayesian Networks (CTBNs) represent a compact yet powerful framework for understanding multivariate time-series data. Given complete data, parameters and structure can be estimated efficiently in closed-form. However, if…

Machine Learning · Statistics 2019-11-04 Dominik Linzner , Michael Schmidt , Heinz Koeppl

Uncertainty quantification is a fundamental yet unsolved problem for deep learning. The Bayesian framework provides a principled way of uncertainty estimation but is often not scalable to modern deep neural nets (DNNs) that have a large…

Machine Learning · Computer Science 2020-08-25 Lingkai Kong , Jimeng Sun , Chao Zhang