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 anomaly or 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 focus on using quantile regression to estimate aleatoric uncertainty and use it for estimating uncertainty in both supervised and unsupervised lesion detection problems. In the unsupervised settings, we apply quantile regression to a lesion detection task using Variational AutoEncoder (VAE). The VAE models the output as a conditionally independent Gaussian characterized by means and variances for each output dimension. Unfortunately, joint optimization of both mean and variance in the VAE leads to the well-known problem of shrinkage or underestimation of variance. We describe an alternative VAE model, Quantile-Regression VAE (QR-VAE), that avoids this variance shrinkage problem by estimating conditional quantiles for the given input image. Using the estimated quantiles, we compute the conditional mean and variance for input images under the conditionally Gaussian model. We then compute reconstruction probability using this model as a principled approach to outlier or anomaly detection applications. In the supervised setting, we develop binary quantile regression (BQR) for the supervised lesion segmentation task. BQR segmentation can capture uncertainty in label boundaries. We show how quantile regression can be used to characterize expert disagreement in the location of lesion boundaries.

翻译：尽管在多种应用中各种机器学习任务上取得了令人印象深刻的先进业绩,但深层次的学习方法可以产生过度自信的预测,特别是培训数据有限。因此,在异常或损伤检测和临床诊断等关键应用中,量化不确定性是特别重要的,在其中,对不确定性进行现实的评估对于确定外科外科边距、疾病状况和适当治疗至关重要。在这项工作中,我们侧重于利用微量回归来估计受监管和不受监督的损伤检测问题的不确定性。在不受监督的环境下,我们使用挥发性自动化自动编码数据分析器(VAE)对测值任务进行定量回归。VAE模型将产出作为有条件独立的高估数字模型,以每种产出层面的手段和差异为特征。不幸的是,对VAE的平均值和差异进行联合优化导致众所周知的缩小或低估差异问题。我们描述了一种替代的 VAE模型、量化性递增性递增 VAE(QR-VAE),从而避免使用该变异性数据模型进行这种变异性分析。