R φqφ(z)dz = 0. Thus, the gradient of the log-variance loss becomes equaltothegradientofthe KL divergence. Therefore, for large enough D, the condition from Proposition 3 (see Eq. 19), is fulfilled and the statement follows immediately. This result isexpected to extend to the multivariate cases as well. For all the experiments listed in the main text, we use the VarGrad estimator for the gradients of the logistic regression models. VarGrad achieves considerable variance reduction over the adaptive (RELAX) and non-adaptive (ControlledReinforce)model-agnosticestimators.

Species range maps (SRMs) are essential tools for research and policy-making in ecology, conservation, and environmental management.

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