8 Supplementary Material

Calculation of T Given data D, disaggregate Y into M equal-size bins, and the m-th bin is denoted as Bm. Let m = |Bm| denote the number of samples in Bm. For distribution p 2 (V A Y) conditioned on y in Bm, pV,A|ym, pV|ym and pA|ym are denoted as the joint distribution of (V,A), marginal distribution of V and A, respectively. As detailed in Section 5.1 of [33] and Algorithm 4 of [32], Um could be calculated through U-statistic. Specifically, in [33], they consider designing kernel as ij(av)= I(Ai = a,Vi = v) I(Ai = a)I(Vi = v), for i and j-th sample in Dt.