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The availability of large training data has led to the development of sophisticated deep learning algorithms to achieve state-of-the-art performance on various tasks and several applications have been benefited immensely. Despite the unparalleled success, the performance of deep learning algorithms depends significantly on the training data distribution. An imbalance in training data distribution affects the performance of deep models. Our research focuses on designing and developing solutions for different real-world problems, specifically related to facial analytic tasks, with imbalanced data distribution. These problems include injured face recognition, fake image detection, and estimation and mitigation of bias in model prediction.