Beta quantile regression for robust estimation of uncertainty in the
  presence of outliers
Haleh Akrami Omar Zamzam Anand Joshi Sergul Aydore Richard Leahy
Quantile Regression (QR) can be used to estimate aleatoric uncertainty in
deep neural networks and can generate prediction intervals. Quantifying
uncertainty is particularly important in critical applications such as clinical
diagnosis, where a realistic assessment of uncertainty is essential in
determining disease status and planning the appropriate treatment. The most
common application of quantile regression models is in cases where the
parametric likelihood cannot be specified. Although quantile regression is
quite robust to outlier response observations, it can be sensitive to outlier
covariate observations (features). Outlier features can compromise the
performance of deep learning regression problems such as style translation,
image reconstruction, and deep anomaly detection, potentially leading to
misleading conclusions. To address this problem, we propose a robust solution
for quantile regression that incorporates concepts from robust divergence. We
compare the performance of our proposed method with (i) least trimmed quantile
regression and (ii) robust regression based on the regularization of
case-specific parameters in a simple real dataset in the presence of outlier.
These methods have not been applied in a deep learning framework. We also
demonstrate the applicability of the proposed method by applying it to a
medical imaging translation task using diffusion models.