Deep learning models (DLMs) can achieve state-of-the-art performance in histopathology image segmentation and classification, but have limited deployment potential in real-world clinical settings. Uncertainty estimates of DLMs can increase trust by identifying predictions and images that need further review. Dice scores and coefficients (Dice) are benchmarks for evaluation of image segmentation performance, but usually not evaluated with DLM uncertainty quantification. This study reports DLM's trained with uncertainty estimations, using ran-domly initialized weights and Monte Carlo dropout, to segment tumors from microscopic Hematoxylin and Eosin dye stained prostate core biopsy histology RGB images. Image level maps showed significant correlation [Spearman's rank (p < 0.05)] between overall and specific prostate tissue image sub-region uncertainties with model performance estimations by Dice. This study reports that linear models that can predict Dice segmentation scores from multiple clinical sub-region based uncertainties of prostate cancer can be a more comprehensive performance evaluation metric without loss in predictive capability of DLMs with a low root mean square error.

Working with any gradient-based machine learning algorithm involves the tedious task of tuning the optimizer's hyperparameters, such as its step size. Recent work has shown how the step size can itself be optimized alongside the model parameters by manually deriving expressions for "hypergradients" ahead of time.We show how to automatically compute hypergradients with a simple and elegant modification to backpropagation. This allows us to easily apply the method to other optimizers and hyperparameters (e.g. momentum coefficients). We can even recursively apply the method to its own hyper-hyperparameters, and so on ad infinitum. As these towers of optimizers grow taller, they become less sensitive to the initial choice of hyperparameters. We present experiments validating this for MLPs, CNNs, and RNNs. Finally, we provide a simple PyTorch implementation of this algorithm (see http://people.csail.mit.edu/kach/gradient-descent-the-ultimate-optimizer).