Optimal Transport (OT) + Fairness (R2, R4): Let us highlight two key differences between "Wasserstein Fair10 Classification" (Jiang et al.) and our work. Generally group fairness constraints31 are trying to reflect a certain independence between the prediction and the sensitive attribute.

Thm. 3.2] we can construct an SCM

The coefficients in this RF expansion are optimized to fit the given data of input-output pairs.

In recent years, transformer-based models have revolutionized deep learning, particularly in sequence modeling.

This illustrates the dependence of the classifier on the representation's robustness, i.e., the predictor can only be robust if

Other concurrent works address, e.g., learning from soft interventions with polynomial mixing [

Despitethis noble goal, it has been acknowledged in the literature that statistical tests based ontheEOareoblivious totheunderlying causal mechanisms thatgenerated the disparity in the first place (Hardt et al. 2016).

Our analysis provides full distribution information on the joint outputs. Furthermore, the9 distribution ofthe cosine similarity explains whymoderately deepand wide ReLU networks can betrained despite10 negative results by mean field (MF) analysis based on correlations. There,14 the normal distribution originates from the MF limit. In contrast, here we understand that the output distribution is15 completely determined bytheempirical covariance matrix ofinputs. This is rather obvious however. Instead, we refer to the rich literature on linear neural networks at23 initialization.

However, SBC has drawbacks: The test statistic is somewhat ad-hoc, interactions are difficult to examine, multiple testing is a challenge, and the resulting p-value is not a divergence metric.