We propose an energy-based framework for correcting mislabelled training examples in the context of binary classification. While existing work addresses random and class-dependent label noise, we focus on feature dependent label noise, which is ubiquitous in real-world data and difficult to model. Two elements distinguish our approach from others: 1) instead of relying on the original feature space, we employ an autoencoder to learn a discriminative representation and 2) we introduce an energy-based formalism for the label correction problem. We prove that a discriminative representation can be learned by training a generative model using a loss function comprised of the difference of energies corresponding to each class. The learned energy value for each training instance is compared to the original training labels and contradictions between energy assignment and training label are used to correct labels. We validate our method across eight datasets, spanning synthetic and realistic settings, and demonstrate the technique's state-of-the-art label correction performance. Furthermore, we derive analytical expressions to show the effect of label noise on the gradients of empirical risk.
This submission proposes an energy-based method to correct mislabelled examples. Intuitively, the authors claim that contradictions between energy and noisy labels can be used to identify label noise. To make the idea reliable, the authors propose to compute the energy by using learned (commonly shared) features. Experiment results look good. The presentation is also clear. My concerns are as follows:
(1) By learning discriminative features and then correcting the label noise, the authors have implicitly assumed that the label noise strongly dependent on the discriminative features. This assumption may be strong as most labels are provided according to the original instance (features). In the experiment section, it is very unclear about how the noise is generated, e.g., how to select x_i according to variance? How to set the threshold? What is "col" in Tables 1 and 2? What are the overall label noise rates? Note that if the threshold for the variance is large. It means that the noise is only added to the discriminative features, making the experiment too ad-hoc. 
(2) The theory of why the residual energy can be used to identify label noise is elusive. How to set the threshold for identifying label noise with a theoretical guarantee is also unclear. Two recent papers on learning with instance-dependent label noise are surprisingly missed, e.g., Menon, Aditya Krishna, Brendan Van Rooyen, and Nagarajan Natarajan. "Learning from binary labels with instance-dependent corruption." arXiv preprint arXiv:1605.00751 (2016). and Cheng, Jiacheng, et al. "Learning with Bounded Instance-and Label-dependent Label Noise." arXiv preprint arXiv:1709.03768 (2017). The latter one proposes algorithms to identify label noise with theoretical guarantees. The authors should compare the proposed method with them.
(3) There are methods provided for choose the values of hyperparameters. Most of them are empirically set, which is not convincing.
(4) The authors reported that with discriminative features learned by employing noisy data, the proposed method also provide good performance. It would be interesting to see how corrected labels will recursively help better learn the discriminative features. Illustrating figures are preferred.