The Optimal Uncertainty Algorithm in the Mystic Framework

We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a framework for the communication and comparison of UQ results. In particular, this framework does not implicitly impose inappropriate assumptions nor does it repudiate relevant information. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that given a set of assumptions and information, there exist bounds on uncertainties obtained as values of optimization problems and that these bounds are optimal. It provides a uniform environment for the optimal solution of the problems of validation, certification, experimental design, reduced order modeling, prediction, extrapolation, all under aleatoric and epistemic uncertainties. OUQ optimization problems are extremely large, and even though under general conditions they have finite-dimensional reductions, they must often be solved numerically. This general algorithmic framework for OUQ has been implemented in the mystic optimization framework. We describe this implementation, and demonstrate its use in the context of the Caltech surrogate model for hypervelocity impact

Bayesian Uncertainty Integration for Model Calibration, Validation, and Prediction

This paper proposes a comprehensive approach to prediction under uncertainty by application to the Sandia National Laboratories verification and validation challenge problem. In this problem, legacy data and experimental measurements of different levels of fidelity and complexity (e.g., coupon tests, material and fluid characterizations, and full system tests/measurements) compose a hierarchy of information where fewer observations are available at higher levels of system complexity. This paper applies a Bayesian methodology in order to incorporate information at different levels of the hierarchy and include the impact of sparse data in the prediction uncertainty for the system of interest. Since separation of aleatory and epistemic uncertainty sources is a pervasive issue in calibration and validation, maintaining this separation in order to perform these activities correctly is the primary focus of this paper. Toward this goal, a Johnson distribution family approach to calibration is proposed in order to enable epistemic and aleatory uncertainty to be separated in the posterior parameter distributions. The model reliability metric approach to validation is then applied, and a novel method of handling combined aleatory and epistemic uncertainty is introduced. The quality of the validation assessment is used to modify the parameter uncertainty and add conservatism to the prediction of interest. Finally, this prediction with its associated uncertainty is used to assess systemlevel reliability (a prediction goal for the challenge problem)

Paying attention to cardiac surgical risk: An interpretable machine learning approach using an uncertainty-aware attentive neural network

Machine learning (ML) is increasingly applied to predict adverse postoperative outcomes in cardiac surgery. Commonly used ML models fail to translate to clinical practice due to absent model explainability, limited uncertainty quantification, and no flexibility to missing data. We aimed to develop and benchmark a novel ML approach, the uncertainty-aware attention network (UAN), to overcome these common limitations. Two Bayesian uncertainty quantification methods were tested, generalized variational inference (GVI) or a posterior network (PN). The UAN models were compared with an ensemble of XGBoost models and a Bayesian logistic regression model (LR) with imputation. The derivation datasets consisted of 153,932 surgery events from the Australian and New Zealand Society of Cardiac and Thoracic Surgeons (ANZSCTS) Cardiac Surgery Database. An external validation consisted of 7343 surgery events which were extracted from the Medical Information Mart for Intensive Care (MIMIC) III critical care dataset. The highest performing model on the external validation dataset was a UAN-GVI with an area under the receiver operating characteristic curve (AUC) of 0.78 (0.01). Model performance improved on high confidence samples with an AUC of 0.81 (0.01). Confidence calibration for aleatoric uncertainty was excellent for all models. Calibration for epistemic uncertainty was more variable, with an ensemble of XGBoost models performing the best with an AUC of 0.84 (0.08). Epistemic uncertainty was improved using the PN approach, compared to GVI. UAN is able to use an interpretable and flexible deep learning approach to provide estimates of model uncertainty alongside stateof- the-art predictions. The model has been made freely available as an easy-to-use web application demonstrating that by designing uncertainty-aware models with innately explainable predictions deep learning may become more suitable for routine clinical use.The ANZSCTS Cardiac Surgery Database Program is funded by the Department of Health (Victoria), the Clinical Excellence Commission (NSW)Queensland Health (QLD)ANZSCTS Database Research activities are supported through a National Health and Medical Research Council Principal Research Fellowship (APP 1136372)Program Grant (APP 1092642

Uncertainty Estimation in One-Stage Object Detection

Environment perception is the task for intelligent vehicles on which all subsequent steps rely. A key part of perception is to safely detect other road users such as vehicles, pedestrians, and cyclists. With modern deep learning techniques huge progress was made over the last years in this field. However such deep learning based object detection models cannot predict how certain they are in their predictions, potentially hampering the performance of later steps such as tracking or sensor fusion. We present a viable approaches to estimate uncertainty in an one-stage object detector, while improving the detection performance of the baseline approach. The proposed model is evaluated on a large scale automotive pedestrian dataset. Experimental results show that the uncertainty outputted by our system is coupled with detection accuracy and the occlusion level of pedestrians

Physics-related epistemic uncertainties in proton depth dose simulation

A set of physics models and parameters pertaining to the simulation of proton energy deposition in matter are evaluated in the energy range up to approximately 65 MeV, based on their implementations in the Geant4 toolkit. The analysis assesses several features of the models and the impact of their associated epistemic uncertainties, i.e. uncertainties due to lack of knowledge, on the simulation results. Possible systematic effects deriving from uncertainties of this kind are highlighted; their relevance in relation to the application environment and different experimental requirements are discussed, with emphasis on the simulation of radiotherapy set-ups. By documenting quantitatively the features of a wide set of simulation models and the related intrinsic uncertainties affecting the simulation results, this analysis provides guidance regarding the use of the concerned simulation tools in experimental applications; it also provides indications for further experimental measurements addressing the sources of such uncertainties.Comment: To be published in IEEE Trans. Nucl. Sc

Concrete Dropout

Dropout is used as a practical tool to obtain uncertainty estimates in large vision models and reinforcement learning (RL) tasks. But to obtain well-calibrated uncertainty estimates, a grid-search over the dropout probabilities is necessary - a prohibitive operation with large models, and an impossible one with RL. We propose a new dropout variant which gives improved performance and better calibrated uncertainties. Relying on recent developments in Bayesian deep learning, we use a continuous relaxation of dropout's discrete masks. Together with a principled optimisation objective, this allows for automatic tuning of the dropout probability in large models, and as a result faster experimentation cycles. In RL this allows the agent to adapt its uncertainty dynamically as more data is observed. We analyse the proposed variant extensively on a range of tasks, and give insights into common practice in the field where larger dropout probabilities are often used in deeper model layers