However, how to evaluate model performance in this challenging task is still unsolved.

In this paper, we study the problem of fair sparse regression on a biased dataset where bias depends upon a hidden binary attribute. The presence of a hidden attribute adds an extra layer of complexity to the problem by combining sparse regression and clustering with unknown binary labels. The corresponding optimization problem is combinatorial, but we propose a novel relaxation of it as an invex optimization problem. To the best of our knowledge, this is the first invex relaxation for a combinatorial problem. We show that the inclusion of the debi-asing/fairness constraint in our model has no adverse effect on the performance. Rather, it enables the recovery of the hidden attribute.

Work done during internship at Google. Work done during visiting-faculty appointment at Google.

The mainstream paradigm for UDA is feature adaptation, a.k.a.

RDP inherits and generalizes the information-theoretic properties of DP . This composition rule, together with Lemma 3, often allows for tighter calculations of (null,δ)-DP for the composed mechanism than directly invoking the strong composition theorem below. Also w.l.o.g., we assume thresholds Substituting the above expression to the definition of RDP and apply Jensen's inequality (6) = The inequality applies Jensen's inequality to bivariate function We use a trick due to [Bun and Steinke, 2016] with some modifications. Now we are ready to prove the three claims of Theorem 8. 13 The claim (3): Substitute the the above bound into Lemma 17, we get: E In the last line, we applied the "indistinguishability" property of an RDP mechanism in Lemma 15 The issue is how to proceed. The proof follows a similar sequence of arguments to that we presented for c = 1 .