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Dropout is conventionally used during the training phase as regularization method and for quantifying uncertainty in deep learning. We propose to use dropout during training as well as inference steps, and average multiple predictions to…

Image and Video Processing · Electrical Eng. & Systems 2023-11-07 Mehmet Yigit Avci , Ziyu Li , Qiuyun Fan , Susie Huang , Berkin Bilgic , Qiyuan Tian

Uncertainty estimation in Neural Networks (NNs) is vital in improving reliability and confidence in predictions, particularly in safety-critical applications. Bayesian Neural Networks (BayNNs) with Dropout as an approximation offer a…

Machine Learning · Computer Science 2024-01-12 Soyed Tuhin Ahmed , Kamal Danouchi , Michael Hefenbrock , Guillaume Prenat , Lorena Anghel , Mehdi B. Tahoori

The deployment of deep neural networks in safety-critical systems necessitates reliable and efficient uncertainty quantification (UQ). A practical and widespread strategy for UQ is repurposing stochastic regularizers as scalable approximate…

Machine Learning · Computer Science 2026-04-15 Adam T. Müller , Tobias Rögelein , Nicolaj C. Stache

Sampling-based methods, e.g., Deep Ensembles and Bayesian Neural Nets have become promising approaches to improve the quality of uncertainty estimation and robust generalization. However, they suffer from a large model size and high latency…

Machine Learning · Computer Science 2024-05-29 Ha Manh Bui , Anqi Liu

The softmax function is a cornerstone of multi-class classification, integral to a wide range of machine learning applications, from large-scale retrieval and ranking models to advanced large language models. However, its computational cost…

Machine Learning · Computer Science 2025-01-16 Jin Chen , Jin Zhang , Xu huang , Yi Yang , Defu Lian , Enhong Chen

We present a new method for uncertainty estimation and out-of-distribution detection in neural networks with softmax output. We extend softmax layer with an additional constant input. The corresponding additional output is able to represent…

Machine Learning · Computer Science 2019-04-09 Marcin Możejko , Mateusz Susik , Rafał Karczewski

Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…

Machine Learning · Computer Science 2021-02-16 Yufei Cui , Wuguannan Yao , Qiao Li , Antoni B. Chan , Chun Jason Xue

Classifying variable stars is key for understanding stellar evolution and galactic dynamics. With the demands of large astronomical surveys, machine learning models, especially attention-based neural networks, have become the…

Instrumentation and Methods for Astrophysics · Physics 2025-07-09 Martina Cádiz-Leyton , Guillermo Cabrera-Vives , Pavlos Protopapas , Daniel Moreno-Cartagena , Cristobal Donoso-Oliva , Ignacio Becker

Accurate uncertainty estimation is crucial for deploying neural networks in risk-sensitive applications such as medical diagnosis. Monte Carlo Dropout is a widely used technique for approximating predictive uncertainty by performing…

Machine Learning · Computer Science 2025-06-05 Tal Zeevi , Ravid Shwartz-Ziv , Yann LeCun , Lawrence H. Staib , John A. Onofrey

The softmax function is widely used in artificial neural networks for the multiclass classification problems, where the softmax transformation enforces the output to be positive and sum to one, and the corresponding loss function allows to…

Machine Learning · Computer Science 2021-12-24 Shaoshi Sun , Zhenyuan Zhang , BoCheng Huang , Pengbin Lei , Jianlin Su , Shengfeng Pan , Jiarun Cao

We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…

Computation · Statistics 2021-05-04 Alex A. Gorodetsky , Gianluca Geraci , Mike Eldred , John D. Jakeman

Recently, deep learning has achieved remarkable successes in medical image analysis. Although deep neural networks generate clinically important predictions, they have inherent uncertainty. Such uncertainty is a major barrier to report…

Image and Video Processing · Electrical Eng. & Systems 2022-06-03 Qing Lyu , Christopher T. Whitlow , Ge Wang

Demand for high-performance, robust, and safe autonomous systems has grown substantially in recent years. These objectives motivate the desire for efficient safety-theoretic reasoning that can be embedded in core decision-making tasks such…

Robotics · Computer Science 2022-12-27 Kristoffer M. Frey , Ted J. Steiner , Jonathan P. How

Whilst an abundance of techniques have recently been proposed to generate counterfactual explanations for the predictions of opaque black-box systems, markedly less attention has been paid to exploring the uncertainty of these generated…

Machine Learning · Computer Science 2021-07-22 Eoin Delaney , Derek Greene , Mark T. Keane

Deep neural networks (NNs) are known for their high-prediction performances. However, NNs are prone to yield unreliable predictions when encountering completely new situations without indicating their uncertainty. Bayesian variants of NNs…

Machine Learning · Computer Science 2023-08-25 Kai Brach , Beate Sick , Oliver Dürr

With the advancements made in deep learning, computer vision problems like object detection and segmentation have seen a great improvement in performance. However, in many real-world applications such as autonomous driving vehicles, the…

Computer Vision and Pattern Recognition · Computer Science 2021-08-10 Kumari Deepshikha , Sai Harsha Yelleni , P. K. Srijith , C Krishna Mohan

Deep neural networks have amply demonstrated their prowess but estimating the reliability of their predictions remains challenging. Deep Ensembles are widely considered as being one of the best methods for generating uncertainty estimates…

Machine Learning · Computer Science 2021-06-28 Nikita Durasov , Timur Bagautdinov , Pierre Baque , Pascal Fua

Missing instances in time series data impose a significant challenge to deep learning models, particularly in regression tasks. In the Earth Observation field, satellite failure or cloud occlusion frequently results in missing time-steps,…

Machine Learning · Computer Science 2025-09-12 Miro Miranda , Francisco Mena , Andreas Dengel

Uncertainty quantification (UQ) includes the characterization, integration, and propagation of uncertainties that result from stochastic variations and a lack of knowledge or data in the natural world. Monte Carlo (MC) method is a…

Methodology · Statistics 2020-11-03 Jiaxin Zhang

Recently, there has been a significant amount of interest in satellite telemetry anomaly detection (AD) using neural networks (NN). For AD purposes, the current approaches focus on either forecasting or reconstruction of the time series,…

Machine Learning · Computer Science 2022-11-29 Mohammad Amin Maleki Sadr , Yeying Zhu , Peng Hu