Comments (1)
CausalForestDML computes a model which is linear in T, roughly
Y = \theta(X) T + \beta(X) + Y_0(X,W)
where theta and beta are forest-based models, and Y_0 is a nuisance function.
So the marginal CATE is just dY/dT = \theta(X). We don't need to compute a gradient because we're assuming linearity in T and the final model is fitting this directly.
For your second question, const_marginal_ate is the average marginal treatment effect over all of the Xs passed in, whereas const_marginal_effect is the per-X heterogeneous treatment effect, so the former is just the mean of the latter (but to be clear, CausalForestDML does not support X=None as a valid input to either method).
Because the treatment effect is assumed to be linear for all of our DML methods, they implement effect in terms of const_marginal_effect (not const_marginal_ate, because again that would average over the treatments instead of giving the heterogeneous effects): effect(X, T0, T1)
is basically just const_marginal_effect(X) @ (T1-T0)
where @
is matrix multiplication.
Again, because the treatment effect is always linear for these models, the marginal effect is the same for any value of T, and marginal_effect(T, X) == const_marginal_effect(X)
and marginal_ate(T, X) == const_marginal_ate(X)
for every T.
Hope that helps.
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