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Estimation of uncertainty in deep learning models is of vital importance,especially in medical imaging, where reliance on inference without taking intoaccount uncertainty could lead to misdiagnosis. Recently, the probabilisticVariational AutoEncoder (VAE) has become a popular model for anomaly detectionin applications such as lesion detection in medical images. The VAE is agenerative graphical model that is used to learn the data distribution fromsamples and then generate new samples from this distribution. By training onnormal samples, the VAE can be used to detect inputs that deviate from thislearned distribution. The VAE models the output as a conditionally independentGaussian characterized by means and variances for each output dimension. VAEscan therefore use reconstruction probability instead of reconstruction errorfor anomaly detection. Unfortunately, joint optimization of both mean andvariance in the VAE leads to the well-known problem of shrinkage orunderestimation of variance. We describe an alternative approach that avoidsthis variance shrinkage problem by using quantile regression. Using estimatedquantiles to compute mean and variance under the Gaussian assumption, wecompute reconstruction probability as a principled approach to outlier oranomaly detection. Results on simulated and Fashion MNIST data demonstrate theeffectiveness of our approach. We also show how our approach can be used forprincipled heterogeneous thresholding for lesion detection in brain images.

Addressing Variance Shrinkage in Variational Autoencoders using Quantile Regression