Machine learning (ML) methods are popular in several application areas of multimedia signal processing. However, most existing solutions in the said area, including the popular least squares, rely on penalizing predictions that deviate from the target ground-truth values. In other words, uncertainty in the ground-truth data is simply ignored. As a result, optimization and validation overemphasize a single-target value when, in fact, human subjects themselves did not unanimously agree to it. This leads to an unreasonable scenario where the trained model is not allowed the benefit of the doubt in terms of prediction accuracy. The problem becomes even more significant in the context of more recent human-centric and immersive multimedia systems where user feedback and interaction are influenced by higher degrees of freedom (leading to higher levels of uncertainty in the ground truth). To ameliorate this drawback, we propose an uncertainty aware loss function (referred to as MSE*) that explicitly accounts for data uncertainty and is useful for both optimization (training) and validation. As examples, we demonstrate the utility of the proposed method for blind estimation of perceptual quality of audiovisual signals, panoramic images, and images affected by camera-induced distortions. The experimental results support the theoretical ideas in terms of reducing prediction errors. The proposed method is also relevant in the context of more recent paradigms, such as crowdsourcing, where larger uncertainty in ground truth is expected. IEEE