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Deep neural networks (DNNs) have achieved tremendous success in a variety of applications across many disciplines. Yet, their superior performance comes with the expensive cost of requiring correctly annotated large-scale datasets. Moreover, due to DNNs' rich capacity, errors in training labels can hamper performance. To combat this problem, mean absolute error (MAE) has recently been proposed as a noise-robust alternative to the commonly-used categorical cross entropy (CCE) loss. However, as we show in this paper, MAE can perform poorly with DNNs and large-scale datasets. Here, we present a theoretically grounded set of noise-robust loss functions that can be seen as a generalization of MAE and CCE. Proposed loss functions can be readily applied with any existing DNN architecture and algorithm, while yielding good performance in a wide range of noisy label scenarios. We report results from experiments conducted with CIFAR-10, CIFAR-100 and FASHION-MNIST datasets and synthetically generated noisy labels.