Akrami Haleh, Joshi Anand A, Aydöre Sergül, Leahy Richard M
Department of Biomedical Engineering, University of Southern California, Los Angeles, USA.
Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, USA.
J Mach Learn Biomed Imaging. 2022;1. Epub 2022 Apr 27.
Despite impressive state-of-the-art performance on a wide variety of machine learning tasks in multiple applications, deep learning methods can produce over-confident predictions, particularly with limited training data. Therefore, quantifying uncertainty is particularly important in critical applications such as lesion detection and clinical diagnosis, where a realistic assessment of uncertainty is essential in determining surgical margins, disease status and appropriate treatment. In this work, we propose a novel approach that uses quantile regression for quantifying aleatoric uncertainty in both supervised and unsupervised lesion detection problems. The resulting confidence intervals can be used for lesion detection and segmentation. In the unsupervised setting, we combine quantile regression with the Variational AutoEncoder (VAE). The VAE is trained on lesion-free data, so when presented with an image with a lesion, it tends to reconstruct a lesion-free version of the image. To detect the lesion, we then compare the input (lesion) and output (lesion-free) images. Here we address the problem of quantifying uncertainty in the images that are reconstructed by the VAE as the basis for principled outlier or lesion detection. The VAE models the output as a conditionally independent Gaussian characterized by its mean and variance. Unfortunately, joint optimization of both mean and variance in the VAE leads to the well-known problem of shrinkage or underestimation of variance. Here we describe an alternative Quantile-Regression VAE (QR-VAE) that avoids this variance shrinkage problem by directly estimating conditional quantiles for the input image. Using the estimated quantiles, we compute the conditional mean and variance for the input image from which we then detect outliers by thresholding at a false-discovery-rate corrected p-value. In the supervised setting, we develop binary quantile regression (BQR) for the supervised lesion segmentation task. We show how BQR can be used to capture uncertainty in lesion boundaries in a manner that characterizes expert disagreement.
尽管深度学习方法在多个应用中的各种机器学习任务上表现出令人印象深刻的先进性能，但它们可能会产生过度自信的预测，尤其是在训练数据有限的情况下。因此，在诸如病变检测和临床诊断等关键应用中，量化不确定性尤为重要，在这些应用中，对不确定性的现实评估对于确定手术切缘、疾病状态和适当治疗至关重要。在这项工作中，我们提出了一种新颖的方法，该方法使用分位数回归来量化监督和无监督病变检测问题中的偶然不确定性。由此产生的置信区间可用于病变检测和分割。在无监督设置中，我们将分位数回归与变分自编码器（VAE）相结合。VAE在无病变数据上进行训练，因此当呈现带有病变的图像时，它倾向于重建该图像的无病变版本。为了检测病变，我们然后比较输入（病变）图像和输出（无病变）图像。在这里，我们解决了量化由VAE重建的图像中的不确定性的问题，以此作为有原则的异常值或病变检测的基础。VAE将输出建模为以其均值和方差为特征的条件独立高斯分布。不幸的是，VAE中均值和方差的联合优化导致了众所周知的方差收缩或低估问题。在这里，我们描述了一种替代的分位数回归VAE（QR-VAE），它通过直接估计输入图像的条件分位数来避免这种方差收缩问题。使用估计的分位数，我们计算输入图像的条件均值和方差，然后通过在错误发现率校正的p值处进行阈值处理来检测异常值。在监督设置中，我们为监督病变分割任务开发了二元分位数回归（BQR）。我们展示了BQR如何以表征专家分歧的方式用于捕获病变边界中的不确定性。
