Robust learning methods aim to learn a clean target distribution from noisy and corrupted training data where a specific corruption pattern is often assumed a priori. Our proposed method can not only successfully learn the clean target distribution from a dirty dataset but also can estimate the underlying noise pattern. To this end, we leverage a mixture-of-experts model that can distinguish two different types of predictive uncertainty, aleatoric and epistemic uncertainty. We show that the ability to estimate the uncertainty plays a significant role in elucidating the corruption patterns as these two objectives are tightly intertwined. We also present a novel validation scheme for evaluating the performance of the corruption pattern estimation. Our proposed method is extensively assessed in terms of both robustness and corruption pattern estimation through a number of domains, including computer vision and natural language processing.