Module cate 

Meta-learners for the conditional average treatment effect τ(x) = E[Y(1) − Y(0) | X = x] of a binary treatment.

learner	idea	reference
SLearner	one model μ(x, d); τ̂ = μ(x,1) − μ(x,0)	—
TLearner	separate μ₀, μ₁ per arm; τ̂ = μ₁ − μ₀	—
XLearner	impute individual effects, model them per arm, blend by propensity	Künzel et al. (2019)
RLearner	residual-on-residual weighted regression (Robinson decomposition)	Nie & Wager (2021)
DrLearner	regress the cross-fitted AIPW pseudo-outcome on x	Kennedy (2023)

The R- and DR-learners cross-fit their nuisances. The DR-learner’s pseudo-outcome is a valid orthogonal signal, so it also supports inference on the CATE through CateFit::blp / CateFit::gate.

Structs

CateFit

A fitted CATE model.

DrLearner

DR-learner (Kennedy, 2023): cross-fit ĝ₀, ĝ₁ and the propensity m̂ exactly as Irm does, form the AIPW pseudo-outcome φ = ĝ₁ − ĝ₀ + D(Y − ĝ₁)/m̂ − (1 − D)(Y − ĝ₀)/(1 − m̂), and regress it on X with the effect learner.

RLearner

R-learner (Nie & Wager, 2021): with cross-fitted m̂(x) = E[Y | X] and propensity ê(x), minimise Σ (Ỹ − τ(X)·D̃)², i.e. a weighted regression of Ỹ/D̃ on X with weights D̃². The effect learner must support Regressor::fit_weighted.

SLearner

S-learner: one outcome model on [x, d].

TLearner

T-learner: separate outcome models for treated and controls.

XLearner

X-learner (Künzel et al., 2019).