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We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic…

Machine Learning · Computer Science 2021-04-06 Richard Archibald , Feng Bao , Yanzhao Cao , He Zhang

Accurate modelling and quantification of predictive uncertainty is crucial in deep learning since it allows a model to make safer decisions when the data is ambiguous and facilitates the users' understanding of the model's confidence in its…

Machine Learning · Statistics 2025-08-26 Soumyasundar Pal , Liheng Ma , Amine Natik , Yingxue Zhang , Mark Coates

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

Methodology · Statistics 2022-10-04 Maoran Xu , Hua Zhou , Yujie Hu , Leo L. Duan

We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the…

Machine Learning · Computer Science 2019-04-25 Yonatan Geifman , Guy Uziel , Ran El-Yaniv

A probabilistic classifier with reliable predictive uncertainties i) fits successfully to the target domain data, ii) provides calibrated class probabilities in difficult regions of the target domain (e.g.\ class overlap), and iii)…

Machine Learning · Computer Science 2022-03-09 Melih Kandemir , Abdullah Akgül , Manuel Haussmann , Gozde Unal

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

Generative models and those with computationally intractable likelihoods are widely used to describe complex systems in the natural sciences, social sciences, and engineering. Fitting these models to data requires likelihood-free inference…

Methodology · Statistics 2025-12-04 Rui Zhang , Oksana A. Chkrebtii , Dongbin Xiu

Decision Focused Learning has emerged as a critical paradigm for integrating machine learning with downstream optimisation. Despite its promise, existing methodologies predominantly rely on probabilistic models and focus narrowly on task…

Machine Learning · Computer Science 2025-03-21 Keivan Shariatmadar , Neil Yorke-Smith , Ahmad Osman , Fabio Cuzzolin , Hans Hallez , David Moens

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

Machine Learning · Computer Science 2020-06-16 Mao Li , Yingyi Ma , Xinhua Zhang

Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

Machine Learning · Statistics 2017-11-07 Balaji Lakshminarayanan , Alexander Pritzel , Charles Blundell

We introduce implicit Bayesian neural networks, a simple and scalable approach for uncertainty representation in deep learning. Standard Bayesian approach to deep learning requires the impractical inference of the posterior distribution…

Machine Learning · Statistics 2020-10-27 Trung Trinh , Samuel Kaski , Markus Heinonen

Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…

Machine Learning · Statistics 2023-12-29 Tim G. J. Rudner , Zonghao Chen , Yee Whye Teh , Yarin Gal

Probabilistic modeling enables combining domain knowledge with learning from data, thereby supporting learning from fewer training instances than purely data-driven methods. However, learning probabilistic models is difficult and has not…

Machine Learning · Computer Science 2017-05-17 Avi Pfeffer

Evidential Deep Learning (EDL) is an emerging method for uncertainty estimation that provides reliable predictive uncertainty in a single forward pass, attracting significant attention. Grounded in subjective logic, EDL derives Dirichlet…

Machine Learning · Computer Science 2024-10-02 Mengyuan Chen , Junyu Gao , Changsheng Xu

A set of novel approaches for estimating epistemic uncertainty in deep neural networks with a single forward pass has recently emerged as a valid alternative to Bayesian Neural Networks. On the premise of informative representations, these…

Computer Vision and Pattern Recognition · Computer Science 2022-07-06 Janis Postels , Mattia Segu , Tao Sun , Luca Sieber , Luc Van Gool , Fisher Yu , Federico Tombari

Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to…

Machine Learning · Statistics 2018-12-03 Andrey Malinin , Mark Gales

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

Machine Learning · Computer Science 2022-02-23 Andrew Wood , Moshik Hershcovitch , Daniel Waddington , Sarel Cohen , Peter Chin

Deep learning has achieved impressive performance on many tasks in recent years. However, it has been found that it is still not enough for deep neural networks to provide only point estimates. For high-risk tasks, we need to assess the…

Machine Learning · Computer Science 2021-04-28 Yuandu Lai , Yucheng Shi , Yahong Han , Yunfeng Shao , Meiyu Qi , Bingshuai Li

There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained…

Computer Vision and Pattern Recognition · Computer Science 2017-10-06 Alex Kendall , Yarin Gal