A.2 DerivationsforSection3.1 We begin with a formal derivation of the formulas in Section 3.1. We remind that we consider a function F(θ) whose parameters can be split inton SI groups: θ = (θ1,...,θn). We solve an optimization problem(1)with projected gradient descent(2). Remark2 The above formulation allegedly lacks the third (divergent) regime. If, conversely, η > 1Pn i=1αi, then at each iteration at least one of the individual ELRs exceeds its convergencethreshold: ηi > 1αi.

For instance, one such notion is'unawareness', which necessitates Additionally, preference-based fairness argues that an algorithm's design should not be solely determined by its creators or regulators but should also incorporate the preferences of those directly A myriad of techniques exist to construct fair models using counterfactual inference. Theorem 2. Assume that R has been generated using Algorithm 2. We have, Pr(R We consider a causal graph shown in Figure 6. The counterfactual data ˇ X were computed by substituting A in the structural function with ˇ A . We implemented our method and the baseline methods as described in Section 5 (since there is no difference between observed data and factual data in this scenario, we have no ICA baseline here). For the CR method, we set the weight of the fairness regularization term as 0.05.

The use of machine learning models in high-stake applications (e.g., healthcare, lending, college admission) has raised growing concerns due to potential biases