Models like LASSO and ridge regression are extensively used in practice due to their interpretability, ease of use, and strong theoretical guarantees.

This section provides the detailed proof for Theorem 1 and the lower bounds of the precision and recall. We derive such theorems with the concentration inequalities in probabilistic theory. In this section, we frequently use the spectral norm. U = I when U is an orthogonal matrix). A.2 Proof of Theorem 1 We deal with some require lemmas which are used for the proof of Theorem 1. Lemma 1. Lemma 3. (David-Kahan sin Theorem) F or given symmetric matrices A, B R Assume that A and A + B have non-negative eigenvalues.

Finally, let us consider (b), the general case. A.2 Proposition 2 Proof We will derive the gradients of the unnormalized posterior since In practice, we recommend the log-sum-exp trick for applying Proposition 2. Let us define Again, let us first consider case (a).

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.