Let $X$ and $Y$ denote the instance and clean label, respectively. When $Y$ is a cause of $X$, according to which many datasets have been constructed, e.g., \textit{SVHN} and \textit{CIFAR}, the distributions of $P(X)$ and $P(Y|X)$ are generally entangled. This means that the unsupervised instances are helpful to learn the classifier and thus reduce the side effect of label noise. However, it remains elusive on how to exploit the causal information to handle the label-noise problem. We propose to model and make use of the causal process in order to correct the label-noise effect.Empirically, the proposed method outperforms all state-of-the-art methods on both synthetic and real-world label-noise datasets.

Appendix A: Derivation Details of evidence lower-bound (ELBO) In this section, we show the derivation details of ELBO(x, y) . Recall that the causal decomposition of the instance-dependent label noise is P ( X, Y,Y,Z) = P (Y)P (Z)P (X |Y,Z)P ( Y | Y,X). In this section, we provide the empirical solution of the ELBO and co-teaching loss. As mentioned in our main paper (see Section 3.2), the negative ELBO loss is to minimize 1). a For co-teaching loss, we directly follow Han et al. [ In this section, we summarize the network structures for different datasets. The source code has been included in our supplementary material.

Let X and Y denote the instance and clean label, respectively. When Y is a cause of X, according to which many datasets have been constructed, e.g., \textit{SVHN} and \textit{CIFAR}, the distributions of P(X) and P(Y X) are generally entangled. This means that the unsupervised instances are helpful to learn the classifier and thus reduce the side effect of label noise. However, it remains elusive on how to exploit the causal information to handle the label-noise problem. We propose to model and make use of the causal process in order to correct the label-noise effect.Empirically, the proposed method outperforms all state-of-the-art methods on both synthetic and real-world label-noise datasets.