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Generalised Bayesian learning algorithms are increasingly popular in machine learning, due to their PAC generalisation properties and flexibility. The present paper aims at providing a self-contained survey on the resulting PAC-Bayes…

Machine Learning · Statistics 2020-02-06 Benjamin Guedj

In the paper, we develop an ensemble-based implicit sampling method for Bayesian inverse problems. For Bayesian inference, the iterative ensemble smoother (IES) and implicit sampling are integrated to obtain importance ensemble samples,…

Numerical Analysis · Mathematics 2018-12-04 Yuming Ba , Lijian Jiang

We introduce a new, efficient, principled and backpropagation-compatible algorithm for learning a probability distribution on the weights of a neural network, called Bayes by Backprop. It regularises the weights by minimising a compression…

Machine Learning · Statistics 2015-05-22 Charles Blundell , Julien Cornebise , Koray Kavukcuoglu , Daan Wierstra

Deep neural network ensembles hold the potential of improving generalization performance for complex learning tasks. This paper presents formal analysis and empirical evaluation to show that heterogeneous deep ensembles with high ensemble…

Computer Vision and Pattern Recognition · Computer Science 2023-10-04 Yanzhao Wu , Ka-Ho Chow , Wenqi Wei , Ling Liu

Neural networks are known to produce poor uncertainty estimations, and a variety of approaches have been proposed to remedy this issue. This includes deep ensemble, a simple and effective method that achieves state-of-the-art results for…

Machine Learning · Computer Science 2022-10-13 Yuesong Shen , Daniel Cremers

In this work we investigate the reasons why Batch Normalization (BN) improves the generalization performance of deep networks. We argue that one major reason, distinguishing it from data-independent normalization methods, is randomness of…

Machine Learning · Computer Science 2018-11-05 Alexander Shekhovtsov , Boris Flach

Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling…

Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…

Machine Learning · Statistics 2026-02-11 Erdong Guo , David Draper

We develop a unified Data Processing Inequality PAC-Bayesian framework -- abbreviated DPI-PAC-Bayesian -- for deriving generalization error bounds in the supervised learning setting. By embedding the Data Processing Inequality (DPI) into…

Information Theory · Computer Science 2025-08-26 Muhan Guan , Farhad Farokhi , Jingge Zhu

Bayesian deep learning (BDL) is a promising approach to achieve well-calibrated predictions on distribution-shifted data. Nevertheless, there exists no large-scale survey that evaluates recent SOTA methods on diverse, realistic, and…

Machine Learning · Computer Science 2023-10-26 Florian Seligmann , Philipp Becker , Michael Volpp , Gerhard Neumann

Transferring a deep neural network trained on one problem to another requires only a small amount of data and little additional computation time. The same behaviour holds for ensembles of deep learning models typically superior to a single…

Machine Learning · Computer Science 2022-06-28 Ilya Shashkov , Nikita Balabin , Evgeny Burnaev , Alexey Zaytsev

In the emerging paradigm of edge learning, neural networks (NNs) are partitioned across distributed edge devices that collaboratively perform inference via wireless transmission. However, deploying NNs for edge inference over wireless…

Information Theory · Computer Science 2026-05-08 Yangshuo He , Guanding Yu , Jingge Zhu

Deep learning based approaches have achieved significant progresses in different tasks like classification, detection, segmentation, and so on. Ensemble learning is widely known to further improve performance by combining multiple…

Computer Vision and Pattern Recognition · Computer Science 2019-05-17 Danlu Chen , Xu-Yao Zhang , Wei Zhang , Yao Lu , Xiuli Li , Tao Mei

Deep Ensembles (DE) are a prominent approach for achieving excellent performance on key metrics such as accuracy, calibration, uncertainty estimation, and out-of-distribution detection. However, hardware limitations of real-world systems…

Ensemble learning combines several individual models to obtain a better generalization performance. In this work we present a practical method for estimating the joint power of several classifiers. It differs from existing approaches which…

Artificial Intelligence · Computer Science 2023-12-22 Simi Haber , Yonatan Wexler

This study investigates Bayesian ensemble learning for improving the quality of decision-making. We consider a decision-maker who selects an action from a set of candidates based on a policy trained using observations. In our setting, we…

Methodology · Statistics 2024-06-14 Masahiro Kato

Uncertainty quantification is central to many applications of causal machine learning, yet principled Bayesian inference for causal effects remains challenging. Standard Bayesian approaches typically require specifying a probabilistic model…

Machine Learning · Statistics 2026-03-04 Emil Javurek , Dennis Frauen , Yuxin Wang , Stefan Feuerriegel

We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models. We further demonstrate that this finding allows us to make meaningful estimates of the model uncertainty using…

Machine Learning · Statistics 2018-07-17 Mattias Teye , Hossein Azizpour , Kevin Smith

This research introduces a novel methodology for optimizing Bayesian Neural Networks (BNNs) by synergistically integrating them with traditional machine learning algorithms such as Random Forests (RF), Gradient Boosting (GB), and Support…

Machine Learning · Computer Science 2023-10-10 Peiwen Tan

Bayesian Neural Networks (BNNs) offer probability distributions for model parameters, enabling uncertainty quantification in predictions. However, they often underperform compared to deterministic neural networks. Utilizing mutual learning…

Machine Learning · Computer Science 2024-07-04 Cuong Pham , Cuong C. Nguyen , Trung Le , Dinh Phung , Gustavo Carneiro , Thanh-Toan Do