OnInductiveBiasesforHeterogeneousTreatment EffectEstimation Appendix

For all considered pseudo-outcomes it holds thatEP [ Yη|X = x] = τ(x) - they are unbiased for CATEwhenηisknown. The testable implications oftheshared structure bias, asencoded byhyperparameters suchasλ2,however,aredifferentfor(i)thePOestimationand(ii) 2 the CATE estimation problems, which is a feature that we would suggest to exploit in choosing hyperparameter settings. Unfortunately,good performance on estimation of the POs is not sufficient. Illustrative results In Figure 1 we present illustrative results on Setup B withn0 = n1 = 2000, and observe that following our heuristic of increasingλ2 until factual performance deteriorates would almost always lead to choosing the best hyperparameter setting; for both hard and flexible approach this suggests a switch fromλ = 10 1 to λ2 = 10 2 as ρ increases1. Therefore, FlexTENet also generalizes the SNet class discussed in [4], which includes PO-specific feature spaces3.