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Uncertainty Quantification in Deep Learning for Safer Neuroimage Enhancement2019-07-31   ${\displaystyle \cong }$
Deep learning (DL) has shown great potential in medical image enhancement problems, such as super-resolution or image synthesis. However, to date, little consideration has been given to uncertainty quantification over the output image. Here we introduce methods to characterise different components of uncertainty in such problems and demonstrate the ideas using diffusion MRI super-resolution. Specifically, we propose to account for $intrinsic$ uncertainty through a heteroscedastic noise model and for $parameter$ uncertainty through approximate Bayesian inference, and integrate the two to quantify $predictive$ uncertainty over the output image. Moreover, we introduce a method to propagate the predictive uncertainty on a multi-channelled image to derived scalar parameters, and separately quantify the effects of intrinsic and parameter uncertainty therein. The methods are evaluated for super-resolution of two different signal representations of diffusion MR images---DTIs and Mean Apparent Propagator MRI---and their derived quantities such as MD and FA, on multiple datasets of both healthy and pathological human brains. Results highlight three key benefits of uncertainty modelling for improving the safety of DL-based image enhancement systems. Firstly, incorporating uncertainty improves the predictive performance even when test data departs from training data. Secondly, the predictive uncertainty highly correlates with errors, and is therefore capable of detecting predictive "failures". Results demonstrate that such an uncertainty measure enables subject-specific and voxel-wise risk assessment of the output images. Thirdly, we show that the method for decomposing predictive uncertainty into its independent sources provides high-level "explanations" for the performance by quantifying how much uncertainty arises from the inherent difficulty of the task or the limited training examples.
Exploring Uncertainty in Deep Learning for Construction of Prediction Intervals2021-04-26   ${\displaystyle \cong }$
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 reliability of the model predictions. This requires us to quantify the uncertainty of model prediction and construct prediction intervals. In this paper, We explore the uncertainty in deep learning to construct the prediction intervals. In general, We comprehensively consider two categories of uncertainties: aleatory uncertainty and epistemic uncertainty. We design a special loss function, which enables us to learn uncertainty without uncertainty label. We only need to supervise the learning of regression task. We learn the aleatory uncertainty implicitly from the loss function. And that epistemic uncertainty is accounted for in ensembled form. Our method correlates the construction of prediction intervals with the uncertainty estimation. Impressive results on some publicly available datasets show that the performance of our method is competitive with other state-of-the-art methods.
STUaNet: Understanding uncertainty in spatiotemporal collective human mobility2021-02-08   ${\displaystyle \cong }$
The high dynamics and heterogeneous interactions in the complicated urban systems have raised the issue of uncertainty quantification in spatiotemporal human mobility, to support critical decision-makings in risk-aware web applications such as urban event prediction where fluctuations are of significant interests. Given the fact that uncertainty quantifies the potential variations around prediction results, traditional learning schemes always lack uncertainty labels, and conventional uncertainty quantification approaches mostly rely upon statistical estimations with Bayesian Neural Networks or ensemble methods. However, they have never involved any spatiotemporal evolution of uncertainties under various contexts, and also have kept suffering from the poor efficiency of statistical uncertainty estimation while training models with multiple times. To provide high-quality uncertainty quantification for spatiotemporal forecasting, we propose an uncertainty learning mechanism to simultaneously estimate internal data quality and quantify external uncertainty regarding various contextual interactions. To address the issue of lacking labels of uncertainty, we propose a hierarchical data turbulence scheme where we can actively inject controllable uncertainty for guidance, and hence provide insights to both uncertainty quantification and weak supervised learning. Finally, we re-calibrate and boost the prediction performance by devising a gated-based bridge to adaptively leverage the learned uncertainty into predictions. Extensive experiments on three real-world spatiotemporal mobility sets have corroborated the superiority of our proposed model in terms of both forecasting and uncertainty quantification.
DEUP: Direct Epistemic Uncertainty Prediction2021-02-16   ${\displaystyle \cong }$
Epistemic uncertainty is the part of out-of-sample prediction error due to the lack of knowledge of the learner. Whereas previous work was focusing on model variance, we propose a principled approach for directly estimating epistemic uncertainty by learning to predict generalization error and subtracting an estimate of aleatoric uncertainty, i.e., intrinsic unpredictability. This estimator of epistemic uncertainty includes the effect of model bias and can be applied in non-stationary learning environments arising in active learning or reinforcement learning. In addition to demonstrating these properties of Direct Epistemic Uncertainty Prediction (DEUP), we illustrate its advantage against existing methods for uncertainty estimation on downstream tasks including sequential model optimization and reinforcement learning. We also evaluate the quality of uncertainty estimates from DEUP for probabilistic classification of images and for estimating uncertainty about synergistic drug combinations.
Validating uncertainty in medical image translation2020-02-11   ${\displaystyle \cong }$
Medical images are increasingly used as input to deep neural networks to produce quantitative values that aid researchers and clinicians. However, standard deep neural networks do not provide a reliable measure of uncertainty in those quantitative values. Recent work has shown that using dropout during training and testing can provide estimates of uncertainty. In this work, we investigate using dropout to estimate epistemic and aleatoric uncertainty in a CT-to-MR image translation task. We show that both types of uncertainty are captured, as defined, providing confidence in the output uncertainty estimates.
Probabilistic Super-Resolution of Solar Magnetograms: Generating Many Explanations and Measuring Uncertainties2019-11-04   ${\displaystyle \cong }$
Machine learning techniques have been successfully applied to super-resolution tasks on natural images where visually pleasing results are sufficient. However in many scientific domains this is not adequate and estimations of errors and uncertainties are crucial. To address this issue we propose a Bayesian framework that decomposes uncertainties into epistemic and aleatoric uncertainties. We test the validity of our approach by super-resolving images of the Sun's magnetic field and by generating maps measuring the range of possible high resolution explanations compatible with a given low resolution magnetogram.
Uncertainty Modelling in Deep Neural Networks for Image Data2020-11-17   ${\displaystyle \cong }$
Quantifying uncertainty in a model's predictions is important as it enables, for example, the safety of an AI system to be increased by acting on the model's output in an informed manner. We cannot expect a system to be 100% accurate or perfect at its task, however, we can equip the system with some tools to inform us if it is not certain about a prediction. This way, a second check can be performed, or the task can be passed to a human specialist. This is crucial for applications where the cost of an error is high, such as in autonomous vehicle control, medical image analysis, financial estimations or legal fields. Deep Neural Networks are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in DNNs is a challenging and yet on-going problem. Although there have been many efforts to equip NNs with tools to estimate uncertainty, such as Monte Carlo Dropout, most of the previous methods only focus on one of the three types of model, data or distributional uncertainty. In this paper we propose a complete framework to capture and quantify all of these three types of uncertainties in DNNs for image classification. This framework includes an ensemble of CNNs for model uncertainty, a supervised reconstruction auto-encoder to capture distributional uncertainty and using the output of activation functions in the last layer of the network, to capture data uncertainty. Finally we demonstrate the efficiency of our method on popular image datasets for classification.
Real-time Uncertainty Decomposition for Online Learning Control2020-10-06   ${\displaystyle \cong }$
Safety-critical decisions based on machine learning models require a clear understanding of the involved uncertainties to avoid hazardous or risky situations. While aleatoric uncertainty can be explicitly modeled given a parametric description, epistemic uncertainty rather describes the presence or absence of training data. This paper proposes a novel generic method for modeling epistemic uncertainty and shows its advantages over existing approaches for neural networks on various data sets. It can be directly combined with aleatoric uncertainty estimates and allows for prediction in real-time as the inference is sample-free. We exploit this property in a model-based quadcopter control setting and demonstrate how the controller benefits from a differentiation between aleatoric and epistemic uncertainty in online learning of thermal disturbances.
Estimating Risk and Uncertainty in Deep Reinforcement Learning2020-02-17   ${\displaystyle \cong }$
We propose a method for disentangling epistemic and aleatoric uncertainties in deep reinforcement learning. Aleatoric uncertainty, or risk, which arises from inherently stochastic environments or agents, must be accounted for in the design of risk-sensitive algorithms. Epistemic uncertainty, which stems from limited data, is important both for risk-sensitivity and for efficient exploration. Our method combines elements from distributional reinforcement learning and approximate Bayesian inference techniques with neural networks, allowing us to disentangle both types of uncertainty on the expected return of a policy. Specifically, the learned return distribution provides the aleatoric uncertainty, and the Bayesian posterior yields the epistemic uncertainty. Although our approach in principle requires a large number of samples from the Bayesian posterior to estimate the epistemic uncertainty, we show that two networks already yield a useful approximation. We perform experiments that illustrate our method and some applications.
Approaching Neural Network Uncertainty Realism2021-01-08   ${\displaystyle \cong }$
Statistical models are inherently uncertain. Quantifying or at least upper-bounding their uncertainties is vital for safety-critical systems such as autonomous vehicles. While standard neural networks do not report this information, several approaches exist to integrate uncertainty estimates into them. Assessing the quality of these uncertainty estimates is not straightforward, as no direct ground truth labels are available. Instead, implicit statistical assessments are required. For regression, we propose to evaluate uncertainty realism -- a strict quality criterion -- with a Mahalanobis distance-based statistical test. An empirical evaluation reveals the need for uncertainty measures that are appropriate to upper-bound heavy-tailed empirical errors. Alongside, we transfer the variational U-Net classification architecture to standard supervised image-to-image tasks. We adopt it to the automotive domain and show that it significantly improves uncertainty realism compared to a plain encoder-decoder model.
Improving model calibration with accuracy versus uncertainty optimization2020-12-14   ${\displaystyle \cong }$
Obtaining reliable and accurate quantification of uncertainty estimates from deep neural networks is important in safety-critical applications. A well-calibrated model should be accurate when it is certain about its prediction and indicate high uncertainty when it is likely to be inaccurate. Uncertainty calibration is a challenging problem as there is no ground truth available for uncertainty estimates. We propose an optimization method that leverages the relationship between accuracy and uncertainty as an anchor for uncertainty calibration. We introduce a differentiable accuracy versus uncertainty calibration (AvUC) loss function that allows a model to learn to provide well-calibrated uncertainties, in addition to improved accuracy. We also demonstrate the same methodology can be extended to post-hoc uncertainty calibration on pretrained models. We illustrate our approach with mean-field stochastic variational inference and compare with state-of-the-art methods. Extensive experiments demonstrate our approach yields better model calibration than existing methods on large-scale image classification tasks under distributional shift.
Regression with Uncertainty Quantification in Large Scale Complex Data2019-12-04   ${\displaystyle \cong }$
While several methods for predicting uncertainty on deep networks have been recently proposed, they do not readily translate to large and complex datasets. In this paper we utilize a simplified form of the Mixture Density Networks (MDNs) to produce a one-shot approach to quantify uncertainty in regression problems. We show that our uncertainty bounds are on-par or better than other reported existing methods. When applied to standard regression benchmark datasets, we show an improvement in predictive log-likelihood and root-mean-square-error when compared to existing state-of-the-art methods. We also demonstrate this method's efficacy on stochastic, highly volatile time-series data where stock prices are predicted for the next time interval. The resulting uncertainty graph summarizes significant anomalies in the stock price chart. Furthermore, we apply this method to the task of age estimation from the challenging IMDb-Wiki dataset of half a million face images. We successfully predict the uncertainties associated with the prediction and empirically analyze the underlying causes of the uncertainties. This uncertainty quantification can be used to pre-process low quality datasets and further enable learning.
Towards calibrated and scalable uncertainty representations for neural networks2019-12-03   ${\displaystyle \cong }$
For many applications it is critical to know the uncertainty of a neural network's predictions. While a variety of neural network parameter estimation methods have been proposed for uncertainty estimation, they have not been rigorously compared across uncertainty measures. We assess four of these parameter estimation methods to calibrate uncertainty estimation using four different uncertainty measures: entropy, mutual information, aleatoric uncertainty and epistemic uncertainty. We evaluate the calibration of these parameter estimation methods using expected calibration error. Additionally, we propose a novel method of neural network parameter estimation called RECAST, which combines cosine annealing with warm restarts with Stochastic Gradient Langevin Dynamics, capturing more diverse parameter distributions. When benchmarked against mutilated image data, we show that RECAST is well-calibrated and when combined with predictive entropy and epistemic uncertainty it offers the best calibrated measure of uncertainty when compared to recent methods.
Objective Evaluation of Deep Uncertainty Predictions for COVID-19 Detection2020-12-22   ${\displaystyle \cong }$
Deep neural networks (DNNs) have been widely applied for detecting COVID-19 in medical images. Existing studies mainly apply transfer learning and other data representation strategies to generate accurate point estimates. The generalization power of these networks is always questionable due to being developed using small datasets and failing to report their predictive confidence. Quantifying uncertainties associated with DNN predictions is a prerequisite for their trusted deployment in medical settings. Here we apply and evaluate three uncertainty quantification techniques for COVID-19 detection using chest X-Ray (CXR) images. The novel concept of uncertainty confusion matrix is proposed and new performance metrics for the objective evaluation of uncertainty estimates are introduced. Through comprehensive experiments, it is shown that networks pertained on CXR images outperform networks pretrained on natural image datasets such as ImageNet. Qualitatively and quantitatively evaluations also reveal that the predictive uncertainty estimates are statistically higher for erroneous predictions than correct predictions. Accordingly, uncertainty quantification methods are capable of flagging risky predictions with high uncertainty estimates. We also observe that ensemble methods more reliably capture uncertainties during the inference.
Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction2021-02-12   ${\displaystyle \cong }$
Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less frequently systematically analyzed. In this work, we introduce a Bayesian variational framework to quantify the epistemic uncertainty. To this end, we solve the linear inverse problem of undersampled MRI reconstruction in a variational setting. The associated energy functional is composed of a data fidelity term and the total deep variation (TDV) as a learned parametric regularizer. To estimate the epistemic uncertainty we draw the parameters of the TDV regularizer from a multivariate Gaussian distribution, whose mean and covariance matrix are learned in a stochastic optimal control problem. In several numerical experiments, we demonstrate that our approach yields competitive results for undersampled MRI reconstruction. Moreover, we can accurately quantify the pixelwise epistemic uncertainty, which can serve radiologists as an additional resource to visualize reconstruction reliability.
Integrating uncertainty in deep neural networks for MRI based stroke analysis2020-08-13   ${\displaystyle \cong }$
At present, the majority of the proposed Deep Learning (DL) methods provide point predictions without quantifying the models uncertainty. However, a quantification of the reliability of automated image analysis is essential, in particular in medicine when physicians rely on the results for making critical treatment decisions. In this work, we provide an entire framework to diagnose ischemic stroke patients incorporating Bayesian uncertainty into the analysis procedure. We present a Bayesian Convolutional Neural Network (CNN) yielding a probability for a stroke lesion on 2D Magnetic Resonance (MR) images with corresponding uncertainty information about the reliability of the prediction. For patient-level diagnoses, different aggregation methods are proposed and evaluated, which combine the single image-level predictions. Those methods take advantage of the uncertainty in image predictions and report model uncertainty at the patient-level. In a cohort of 511 patients, our Bayesian CNN achieved an accuracy of 95.33% at the image-level representing a significant improvement of 2% over a non-Bayesian counterpart. The best patient aggregation method yielded 95.89% of accuracy. Integrating uncertainty information about image predictions in aggregation models resulted in higher uncertainty measures to false patient classifications, which enabled to filter critical patient diagnoses that are supposed to be closer examined by a medical doctor. We therefore recommend using Bayesian approaches not only for improved image-level prediction and uncertainty estimation but also for the detection of uncertain aggregations at the patient-level.
Interval Deep Learning for Uncertainty Quantification in Safety Applications2021-05-13   ${\displaystyle \cong }$
Deep neural networks (DNNs) are becoming more prevalent in important safety-critical applications, where reliability in the prediction is paramount. Despite their exceptional prediction capabilities, current DNNs do not have an implicit mechanism to quantify and propagate significant input data uncertainty -- which is common in safety-critical applications. In many cases, this uncertainty is epistemic and can arise from multiple sources, such as lack of knowledge about the data generating process, imprecision, ignorance, and poor understanding of physics phenomena. Recent approaches have focused on quantifying parameter uncertainty, but approaches to end-to-end training of DNNs with epistemic input data uncertainty are more limited and largely problem-specific. In this work, we present a DNN optimized with gradient-based methods capable to quantify input and parameter uncertainty by means of interval analysis, which we call Deep Interval Neural Network (DINN). We perform experiments on an air pollution dataset with sensor uncertainty and show that the DINN can produce accurate bounded estimates from uncertain input data.
Selective Dyna-style Planning Under Limited Model Capacity2020-07-29   ${\displaystyle \cong }$
In model-based reinforcement learning, planning with an imperfect model of the environment has the potential to harm learning progress. But even when a model is imperfect, it may still contain information that is useful for planning. In this paper, we investigate the idea of using an imperfect model selectively. The agent should plan in parts of the state space where the model would be helpful but refrain from using the model where it would be harmful. An effective selective planning mechanism requires estimating predictive uncertainty, which arises out of aleatoric uncertainty, parameter uncertainty, and model inadequacy, among other sources. Prior work has focused on parameter uncertainty for selective planning. In this work, we emphasize the importance of model inadequacy. We show that heteroscedastic regression can signal predictive uncertainty arising from model inadequacy that is complementary to that which is detected by methods designed for parameter uncertainty, indicating that considering both parameter uncertainty and model inadequacy may be a more promising direction for effective selective planning than either in isolation.
Finding novelty with uncertainty2020-02-11   ${\displaystyle \cong }$
Medical images are often used to detect and characterize pathology and disease; however, automatically identifying and segmenting pathology in medical images is challenging because the appearance of pathology across diseases varies widely. To address this challenge, we propose a Bayesian deep learning method that learns to translate healthy computed tomography images to magnetic resonance images and simultaneously calculates voxel-wise uncertainty. Since high uncertainty occurs in pathological regions of the image, this uncertainty can be used for unsupervised anomaly segmentation. We show encouraging experimental results on an unsupervised anomaly segmentation task by combining two types of uncertainty into a novel quantity we call scibilic uncertainty.
Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision2020-04-07   ${\displaystyle \cong }$
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, for example in automotive applications. In Bayesian deep learning, predictive uncertainty is commonly decomposed into the distinct types of aleatoric and epistemic uncertainty. The former can be estimated by letting a neural network output the parameters of a certain probability distribution. Epistemic uncertainty estimation is a more challenging problem, and while different scalable methods recently have emerged, no extensive comparison has been performed in a real-world setting. We therefore accept this task and propose a comprehensive evaluation framework for scalable epistemic uncertainty estimation methods in deep learning. Our proposed framework is specifically designed to test the robustness required in real-world computer vision applications. We also apply this framework to provide the first properly extensive and conclusive comparison of the two current state-of-the-art scalable methods: ensembling and MC-dropout. Our comparison demonstrates that ensembling consistently provides more reliable and practically useful uncertainty estimates. Code is available at https://github.com/fregu856/evaluating_bdl.