We begin by introducing notation. In the main paper (Section 3), we show how to approximate instance-dependent transition matrix by exploiting part-dependent transition matrices. Note that it is more realistic that different instances have different flip rates. However, it is hard to identify these parameters without any assumption. In the main paper (Section 4), we present the experimental results on four synthetic noisy datasets, i.e., F-MNIST, SVHN, CIF AR-10, and NEWS .

The transition matrices for parts can be learned by exploiting anchor points (i.e., data points that belong to a specific class almost surely).

We thank all reviewers for providing us valuable and insightful comments. Below, we answer all of the questions. R1 Q1) The main assumption in this method for part-dependent label noise is not realistic. Thus, we believe the assumption makes sense in reality. Q2) When the deep model is trained using the noisy labels, the features maybe not the accurate or reliable features.

Learning from crowds describes that the annotations of training data are obtained with crowd-sourcing services. Multiple annotators each complete their own small part of the annotations, where labeling mistakes that depend on annotators occur frequently. Modeling the label-noise generation process by the noise transition matrix is a power tool to tackle the label noise. In real-world crowd-sourcing scenarios, noise transition matrices are both annotator- and instance-dependent. However, due to the high complexity of annotator- and instance-dependent transition matrices (AIDTM), annotation sparsity, which means each annotator only labels a little part of instances, makes modeling AIDTM very challenging. Prior works simplify the problem by assuming the transition matrix is instance-independent or using simple parametric ways, which lose modeling generality. Motivated by this, we target a more realistic problem, estimating general AIDTM in practice. Without losing modeling generality, we parameterize AIDTM with deep neural networks. To alleviate the modeling challenge, we suppose every annotator shares its noise pattern with similar annotators, and estimate AIDTM via knowledge transfer. We hence first model the mixture of noise patterns by all annotators, and then transfer this modeling to individual annotators. Furthermore, considering that the transfer from the mixture of noise patterns to individuals may cause two annotators with highly different noise generations to perturb each other, we employ the knowledge transfer between identified neighboring annotators to calibrate the modeling. Theoretical analyses are derived to demonstrate that both the knowledge transfer from global to individuals and the knowledge transfer between neighboring individuals can help model general AIDTM. Experiments confirm the superiority of the proposed approach on synthetic and real-world crowd-sourcing data.

Learning with the \textit{instance-dependent} label noise is challenging, because it is hard to model such real-world noise. Note that there are psychological and physiological evidences showing that we humans perceive instances by decomposing them into parts. Annotators are therefore more likely to annotate instances based on the parts rather than the whole instances. Motivated by this human cognition, in this paper, we approximate the instance-dependent label noise by exploiting \textit{parts-dependent} label noise. Specifically, since instances can be approximately reconstructed by a combination of parts, we approximate the instance-dependent \textit{transition matrix} for an instance by a combination of the transition matrices for the parts of the instance. The transition matrices for parts can be learned by exploiting anchor points (i.e., data points that belong to a specific class almost surely). Empirical evaluations on synthetic and real-world datasets demonstrate our method is superior to the state-of-the-art approaches for learning from the instance-dependent label noise.