Explanation and Use of Uncertainty Quantified by Bayesian Neural Network Classifiers for Breast Histopathology Images

Despite the promise of Convolutional neural network (CNN) based classification models for histopathological images, it is infeasible to quantify its uncertainties. Moreover, CNNs may suffer from overfitting when the data is biased. We show that Bayesian-CNN can overcome these limitations by regularizing automatically and by quantifying the uncertainty. We have developed a novel technique to utilize the uncertainties provided by the Bayesian-CNN that significantly improves the performance on a large fraction of the test data (about 6% improvement in accuracy on 77% of test data). Further, we provide a novel explanation for the uncertainty by projecting the data into a low dimensional space through a nonlinear dimensionality reduction technique. This dimensionality reduction enables interpretation of the test data through visualization and reveals the structure of the data in a low dimensional feature space. We show that the Bayesian-CNN can perform much better than the state-of-the-art transfer learning CNN (TL-CNN) by reducing the false negative and false positive by 11% and 7.7% respectively for the present data set. It achieves this performance with only 1.86 million parameters as compared to 134.33 million for TL-CNN. Besides, we modify the Bayesian-CNN by introducing a stochastic adaptive activation function. The modified Bayesian-CNN performs slightly better than Bayesian-CNN on all performance metrics and significantly reduces the number of false negatives and false positives (3% reduction for both). We also show that these results are statistically significant by performing McNemar's statistical significance test. This work shows the advantages of Bayesian-CNN against the state-of-the-art, explains and utilizes the uncertainties for histopathological images. It should find applications in various medical image classifications.