  Organizations that own data face increasing legal liability for its
discriminatory use against protected demographic groups, extending to
contractual transactions involving third parties access and use of the data.
This is problematic, since the original data owner cannot ex-ante anticipate
all its future uses by downstream users. This paper explores the upstream
ability to preemptively remove the correlations between features and sensitive
attributes by mapping features to a fair representation space. Our main result
shows that the fairness measured by the demographic parity of the
representation distribution can be certified from a finite sample if and only
if the chi-squared mutual information between features and representations is
finite. Empirically, we find that smoothing the representation distribution
provides generalization guarantees of fairness certificates, which improves
upon existing fair representation learning approaches. Moreover, we do not
observe that smoothing the representation distribution degrades the accuracy of
downstream tasks compared to state-of-the-art methods in fair representation
learning.
