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The presence of label noise often misleads the training of deep neural networks. Departing from the recent literature which largely assumes the label noise rate is only determined by the true label class, the errors in human-annotated labels are more likely to be dependent on the difficulty levels of tasks, resulting in settings with instance-dependent label noise. We first provide evidences that the heterogeneous instance-dependent label noise is effectively down-weighting the examples with higher noise rates in a non-uniform way and thus causes imbalances, rendering the strategy of directly applying methods for class-dependent label noise questionable. Built on a recent work peer loss [24], we then propose and study the potentials of a second-order approach that leverages the estimation of several covariance terms defined between the instance-dependent noise rates and the Bayes optimal label. We show that this set of second-order statistics successfully captures the induced imbalances. We further proceed to show that with the help of the estimated second-order statistics, we identify a new loss function whose expected risk of a classifier under instance-dependent label noise is equivalent to a new problem with only class-dependent label noise. This fact allows us to apply existing solutions to handle this better-studied setting. We provide an efficient procedure to estimate these second-order statistics without accessing either ground truth labels or prior knowledge of the noise rates. Experiments on CIFAR10 and CIFAR100 with synthetic instance-dependent label noise and Clothing1M with real-world human label noise verify our approach. Our implementation is available at https://github.com/UCSC-REAL/CAL.