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Uncertainty quantification (UQ) methods play a pivotal role in reducing the impact of uncertainties during both optimization and decision making processes. They have been applied to solve a variety of real-world problems in science and engineering. Bayesian approximation and ensemble learning techniques are two widely-used types of uncertainty quantification (UQ) methods. In this regard, researchers have proposed different UQ methods and examined their performance in a variety of applications such as computer vision (e.g., self-driving cars and object detection), image processing (e.g., image restoration), medical image analysis (e.g., medical image classification and segmentation), natural language processing (e.g., text classification, social media texts and recidivism risk-scoring), bioinformatics, etc. This study reviews recent advances in UQ methods used in deep learning, investigates the application of these methods in reinforcement learning, and highlights fundamental research challenges and directions associated with UQ.

Accurate automated medical image recognition, including classification and segmentation, is one of the most challenging tasks in medical image analysis. Recently, deep learning methods have achieved remarkable success in medical image classification and segmentation, clearly becoming the state-of-the-art methods. However, most of these methods are unable to provide uncertainty quantification (UQ) for their output, often being overconfident, which can lead to disastrous consequences. Bayesian Deep Learning (BDL) methods can be used to quantify uncertainty of traditional deep learning methods, and thus address this issue. We apply three uncertainty quantification methods to deal with uncertainty during skin cancer image classification. They are as follows: Monte Carlo (MC) dropout, Ensemble MC (EMC) dropout and Deep Ensemble (DE). To further resolve the remaining uncertainty after applying the MC, EMC and DE methods, we describe a novel hybrid dynamic BDL model, taking into account uncertainty, based on the Three-Way Decision (TWD) theory. The proposed dynamic model enables us to use different UQ methods and different deep neural networks in distinct classification phases. So, the elements of each phase can be adjusted according to the dataset under consideration. In this study, two best UQ methods (i.e., DE and EMC) are applied in two classification phases (the first and second phases) to analyze two well-known skin cancer datasets, preventing one from making overconfident decisions when it comes to diagnosing the disease. The accuracy and the F1-score of our final solution are, respectively, 88.95% and 89.00% for the first dataset, and 90.96% and 91.00% for the second dataset. Our results suggest that the proposed TWDBDL model can be used effectively at different stages of medical image analysis.