Title: Do We Really Achieve Fairness with Explicit Sensitive Attributes? . Abstract: Recently the wide usage of machine learning models for high-stake decision-making raises the concerns about the fairness and discrimination issue. Existing works found that sensitive information of a sample could be leaked completely by sensitive attributes or partially by non-sensitive attributes, thus removing the sensitive attributes directly from the original features can not achieve fairness. The current fairness practice is to leverage the explicit sensitive attributes (i.e., as regularization) to debias the prediction, based on a strong assumption that non-sensitive attributes of all samples leak the sensitive information totally. However, we investigate the distribution of leaked sensitive information from non-sensitive attributes and make interesting findings that 1) the sensitive information distinctly varies across different samples. 2) the violation of demographic parity for samples prone to leak sensitive information (high-sensitive) are worse than that for low-sensitive samples, indicating the failure of current demographic parity measurements. To this end, we propose a new group fairness ($\alpha$-Demographic Parity) to measure the demographic parity for samples with different levels of sensitive information leakage. Furthermore, we move one step forward and propose to achieve $\alpha$-demographic parity by encouraging the independence of the distribution of the sensitive information in non-sensitive attributes and that of  downstream task prediction, which is formulated as a cross-task knowledge distillation framework. Specifically, the sensitive teacher models the distribution of the sensitive information and the fair student models the distribution of the downstream task prediction. Then we encourage the independence between them by minimizing the Hilbert-Schmidt Independence Criterion. Our model can naturally tackle the limited sensitive attribution scenario since the teacher models can be trained with partial samples with sensitive attributes. Extensive experiments show the superior performance of our proposed method on the $\alpha$-demographic parity and performs well on limited sensitive attribute scenarios.