The accurate estimation of predictive uncertainty carries importance in medical scenarios such as lung node segmentation. Unfortunately, most existing works on predictive uncertainty do not return calibrated uncertainty estimates, which could be used in practice. In this work we exploit multi-grader annotation variability as a source of 'groundtruth' aleatoric uncertainty, which can be treated as a target in a supervised learning problem. We combine this groundtruth uncertainty with a Probabilistic U-Net and test on the LIDC-IDRI lung nodule CT dataset and MICCAI2012 prostate MRI dataset. We find that we are able to improve predictive uncertainty estimates. We also find that we can improve sample accuracy and sample diversity.
Current techniques for estimating aleatoric and epistemic uncertainty follow similar line. In Tanno @cite_4 the authors treat MRI superresolution as a regression problem. They build a CNN directly outputting @math and @math . They model epistemic uncertainty using variational dropout @cite_7 . Bragman @cite_6 build on this technique, applying it to radiotherapy-treatment planning and multi-task learning. Concurrent to @cite_4 Kendall and Gal proposed a similar method using Monte Carlo (MC) instead of variational dropout @cite_12 .They also proposed a method which would work for classification, where they predict a mean and variance in the logit-space just before a sigmoid. Jungo @cite_19 estimate epistemic uncertainty in the context of postoperative brain tumor cavity segmentation using MC dropout @cite_12 . In @cite_18 Ayhan and Berens treat the data augmentation process as part of the approximate posterior @math . They claim this is aleatoric uncertainty, but from their method it appears they really compute epistemic uncertainty. None of these works quantitatively evaluates the quality of the epistemic and aleatoric uncertainties. In this work, we show that the aleatoric uncertainty can indeed be measured.
@cite_18 @cite_4 @cite_7 @cite_6 @cite_19 @cite_12
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In this work, we investigate the value of uncertainty modelling in 3D super-resolution with convolutional neural networks (CNNs). Deep learning has shown success in a plethora of medical image transformation problems, such as super-resolution (SR) and image synthesis. However, the highly ill-posed nature of such problems results in inevitable ambiguity in the learning of networks. We propose to account for intrinsic uncertainty through a per-patch heteroscedastic noise model and for parameter uncertainty through approximate Bayesian inference in the form of variational dropout. We show that the combined benefits of both lead to the state-of-the-art performance SR of diffusion MR brain images in terms of errors compared to ground truth. We further show that the reduced error scores produce tangible benefits in downstream tractography. In addition, the probabilistic nature of the methods naturally confers a mechanism to quantify uncertainty over the super-resolved output. We demonstrate through experiments on both healthy and pathological brains the potential utility of such an uncertainty measure in the risk assessment of the super-resolved images for subsequent clinical use. We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the mini-batch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gaussian dropout objectives correspond to SGVB with local reparameterization, a scale-invariant prior and proportionally fixed posterior variance. Our method allows inference of more flexibly parameterized posteriors; specifically, we propose variational dropout, a generalization of Gaussian dropout where the dropout rates are learned, often leading to better models. The method is demonstrated through several experiments. Uncertainty estimates of modern neuronal networks provide additional information next to the computed predictions and are thus expected to improve the understanding of the underlying model. Reliable uncertainties are particularly interesting for safety-critical computer-assisted applications in medicine, e.g., neurosurgical interventions and radiotherapy planning. We propose an uncertainty-driven sanity check for the identification of segmentation results that need particular expert review. Our method uses a fully-convolutional neural network and computes uncertainty estimates by the principle of Monte Carlo dropout. We evaluate the performance of the proposed method on a clinical dataset with 30 postoperative brain tumor images. The method can segment the highly inhomogeneous resection cavities accurately (Dice coefficients 0.792 @math 0.154). Furthermore, the proposed sanity check is able to detect the worst segmentation and three out of the four outliers. The results highlight the potential of using the additional information from the model's parameter uncertainty to validate the segmentation performance of a deep learning model. Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded framework to reason about model uncertainty, but usually come with a prohibitive computational cost. In this paper we develop a new theoretical framework casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes. A direct result of this theory gives us tools to model uncertainty with dropout NNs - extracting information from existing models that has been thrown away so far. This mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy. We perform an extensive study of the properties of dropout's uncertainty. Various network architectures and nonlinearities are assessed on tasks of regression and classification, using MNIST as an example. We show a considerable improvement in predictive log-likelihood and RMSE compared to existing state-of-the-art methods, and finish by using dropout's uncertainty in deep reinforcement learning.