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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

Increasingly high-stakes decisions are made using neural networks in order to make predictions. Specifically, meteorologists and hedge funds apply these techniques to time series data. When it comes to prediction, there are certain…

Machine Learning · Computer Science 2022-11-14 Levente Foldesi , Matias Valdenegro-Toro

In this work, we investigate Batch Normalization technique and propose its probabilistic interpretation. We propose a probabilistic model and show that Batch Normalization maximazes the lower bound of its marginalized log-likelihood. Then,…

Machine Learning · Statistics 2018-03-22 Andrei Atanov , Arsenii Ashukha , Dmitry Molchanov , Kirill Neklyudov , Dmitry Vetrov

Uncertainty estimation is important for ensuring safety and robustness of AI systems. While most research in the area has focused on un-structured prediction tasks, limited work has investigated general uncertainty estimation approaches for…

Machine Learning · Statistics 2021-02-12 Andrey Malinin , Mark Gales

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

Quantifying the robustness of neural networks or verifying their safety properties against input uncertainties or adversarial attacks have become an important research area in learning-enabled systems. Most results concentrate around the…

Systems and Control · Electrical Eng. & Systems 2019-10-11 Mahyar Fazlyab , Manfred Morari , George J. Pappas

The growing integration of large language models across professional domains transforms how experts make critical decisions in healthcare, education, and law. While significant research effort focuses on getting these systems to communicate…

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…

Optimization and Control · Mathematics 2021-09-10 Marc Goerigk , Jannis Kurtz

When agents devise plans for execution in the real world, they face two important forms of uncertainty: they can never have complete knowledge about the state of the world, and they do not have complete control, as the effects of their…

Artificial Intelligence · Computer Science 2013-02-28 Ron Davidson , Michael R. Fehling

Bridging continuous perceptual signals and discrete symbolic reasoning is a fundamental challenge in AI systems that must operate under uncertainty. We present a neuro-symbolic framework that explicitly models and propagates uncertainty…

Artificial Intelligence · Computer Science 2025-11-19 Jiahao Wu , Shengwen Yu

Cross-modal Retrieval methods build similarity relations between vision and language modalities by jointly learning a common representation space. However, the predictions are often unreliable due to the Aleatoric uncertainty, which is…

Computer Vision and Pattern Recognition · Computer Science 2024-01-17 Hao Li , Jingkuan Song , Lianli Gao , Xiaosu Zhu , Heng Tao Shen

Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over…

Machine Learning · Statistics 2020-12-08 Javier Antorán , James Urquhart Allingham , José Miguel Hernández-Lobato

Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. However, they are often overconfident in their predictions, which leads to inaccurate and miscalibrated…

Machine Learning · Computer Science 2021-02-23 Jeffrey Willette , Juho Lee , Sung Ju Hwang

Trustworthy artificial intelligence increasingly relies on probabilistic computation to achieve robustness, interpretability, security and privacy. In practical systems, such workloads interleave deterministic data access with repeated…

Machine Learning · Computer Science 2026-03-27 Xueji Zhao , Likai Pei , Jianbo Liu , Kai Ni , Ningyuan Cao

Probabilistic forecasting of multivariate time series is essential for various downstream tasks. Most existing approaches rely on the sequences being uniformly spaced and aligned across all variables. However, real-world multivariate time…

Machine Learning · Computer Science 2025-02-18 Yijun Li , Cheuk Hang Leung , Qi Wu

A particularly challenging problem in AI safety is providing guarantees on the behavior of high-dimensional autonomous systems. Verification approaches centered around reachability analysis fail to scale, and purely statistical approaches…

Artificial Intelligence · Computer Science 2025-03-11 Souradeep Dutta , Michele Caprio , Vivian Lin , Matthew Cleaveland , Kuk Jin Jang , Ivan Ruchkin , Oleg Sokolsky , Insup Lee

Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…

Computation · Statistics 2024-11-13 Zahra Moslemi , Yang Meng , Shiwei Lan , Babak Shahbaba

Probabilistic models often use neural networks to control their predictive uncertainty. However, when making out-of-distribution (OOD)} predictions, the often-uncontrollable extrapolation properties of neural networks yield poor uncertainty…

Machine Learning · Computer Science 2022-01-19 Pierre Segonne , Yevgen Zainchkovskyy , Søren Hauberg

Modern weather forecast models perform uncertainty quantification using ensemble prediction systems, which collect nonparametric statistics based on multiple perturbed simulations. To provide accurate estimation, dozens of such…

Machine Learning · Computer Science 2019-12-06 Peter Grönquist , Tal Ben-Nun , Nikoli Dryden , Peter Dueben , Luca Lavarini , Shigang Li , Torsten Hoefler

Neural networks are powerful tools in various applications, and quantifying their uncertainty is crucial for reliable decision-making. In the deep learning field, the uncertainties are usually categorized into aleatoric (data) and epistemic…

Machine Learning · Computer Science 2023-12-21 Wang Zhang , Ziwen Ma , Subhro Das , Tsui-Wei Weng , Alexandre Megretski , Luca Daniel , Lam M. Nguyen