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Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for…

Numerical Analysis · Mathematics 2023-12-07 Siddhartha Mishra , Roberto Molinaro

Deep neural networks have achieved substantial achievements in several computer vision areas, but have vulnerabilities that are often fooled by adversarial examples that are not recognized by humans. This is an important issue for security…

Computer Vision and Pattern Recognition · Computer Science 2021-01-29 Hakmin Lee , Hong Joo Lee , Seong Tae Kim , Yong Man Ro

The advent of fast sensing technologies allows for real-time model updates in many applications where the model parameters are uncertain. Bayesian algorithms, such as ensemble smoothers, offer a real-time probabilistic inversion accounting…

Geophysics · Physics 2022-05-26 Muzammil Hussain Rammay , Sergey Alyaev , Ahmed H Elsheikh

Many dynamic ensemble selection (DES) methods are known in the literature. A previously-developed by the authors, method consists in building a randomized classifier which is treated as a model of the base classifier. The model is…

Machine Learning · Computer Science 2021-09-17 Pawel Trajdos , Marek Kurzynski

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

Machine Learning · Statistics 2019-05-28 Aliaksandr Hubin , Geir Storvik

Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assign to base models a set of deterministic, constant model weights that (1) do not fully account for individual models' varying accuracy…

Methodology · Statistics 2019-04-02 Jeremiah Zhe Liu , John Paisley , Marianthi-Anna Kioumourtzoglou , Brent A. Coull

Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…

Machine Learning · Computer Science 2019-05-28 Manikanta Srikar Yellapragada , Chandra Prakash Konkimalla

This paper investigates novel classifier ensemble techniques for uncertainty calibration applied to various deep neural networks for image classification. We evaluate both accuracy and calibration metrics, focusing on Expected Calibration…

Computer Vision and Pattern Recognition · Computer Science 2025-01-20 Michael Schulze , Nikolas Ebert , Laurenz Reichardt , Oliver Wasenmüller

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…

Machine Learning · Statistics 2023-08-31 Ali Mohammad-Djafari , Ning Chu , Li Wang , Liang Yu

Ensembling deep learning models is a shortcut to promote its implementation in new scenarios, which can avoid tuning neural networks, losses and training algorithms from scratch. However, it is difficult to collect sufficient accurate and…

Machine Learning · Computer Science 2020-12-04 Jun Yang , Fei Wang

Deep Neural Networks (DNNs) have obtained impressive performance across tasks, however they still remain as black boxes, e.g., hard to theoretically analyze. At the same time, Polynomial Networks (PNs) have emerged as an alternative method…

Computer Vision and Pattern Recognition · Computer Science 2023-03-27 Grigorios G Chrysos , Bohan Wang , Jiankang Deng , Volkan Cevher

Deep Neural Networks (DNNs) often rely on very large datasets for training. Given the large size of such datasets, it is conceivable that they contain certain samples that either do not contribute or negatively impact the DNN's…

Machine Learning · Computer Science 2020-11-10 Kashyap Chitta , Jose M. Alvarez , Elmar Haussmann , Clement Farabet

Ensemble learning has gain attention in resent deep learning research as a way to further boost the accuracy and generalizability of deep neural network (DNN) models. Recent ensemble training method explores different training algorithms or…

Machine Learning · Computer Science 2023-01-20 Jingchi Zhang , Huanrui Yang , Hai Li

While deep neural networks have become the go-to approach in computer vision, the vast majority of these models fail to properly capture the uncertainty inherent in their predictions. Estimating this predictive uncertainty can be crucial,…

Machine Learning · Computer Science 2020-04-08 Fredrik K. Gustafsson , Martin Danelljan , Thomas B. Schön

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

This paper addresses the prediction stability, prediction accuracy and control capability of the current probabilistic model-based reinforcement learning (MBRL) built on neural networks. A novel approach dropout-based probabilistic…

Systems and Control · Electrical Eng. & Systems 2023-09-21 Wenjun Huang , Yunduan Cui , Huiyun Li , Xinyu Wu

Machine learning-based Deepfake detection models have achieved impressive results on benchmark datasets, yet their performance often deteriorates significantly when evaluated on out-of-distribution data. In this work, we investigate an…

Computer Vision and Pattern Recognition · Computer Science 2025-07-09 Haroon Wahab , Hassan Ugail , Lujain Jaleel

Deterministic neural networks (NNs) are increasingly being deployed in safety critical domains, where calibrated, robust, and efficient measures of uncertainty are crucial. In this paper, we propose a novel method for training non-Bayesian…

Machine Learning · Computer Science 2020-11-25 Alexander Amini , Wilko Schwarting , Ava Soleimany , Daniela Rus

Neural Processes (NPs) are deep probabilistic models that represent stochastic processes by conditioning their prior distributions on a set of context points. Despite their advantages in uncertainty estimation for complex distributions, NPs…

Machine Learning · Computer Science 2025-06-04 Xuesong Wang , He Zhao , Edwin V. Bonilla

Recently, deep unfolding methods that guide the design of deep neural networks (DNNs) through iterative algorithms have received increasing attention in the field of inverse problems. Unlike general end-to-end DNNs, unfolding methods have…

Optimization and Control · Mathematics 2022-11-28 Zhuo-Xu Cui , Qingyong Zhu , Jing Cheng , Dong Liang