AIPW

Cross-fit augmented inverse-probability weighting

from _api_doc_utils import *

1 Where it fits

Group: Causal inference

AIPW estimates a binary-treatment ATE by combining outcome regressions and a propensity model:

\[ \hat\tau = n^{-1}\sum_i \left[\hat\mu_1(x_i)-\hat\mu_0(x_i) + \frac{d_i(y_i-\hat\mu_1(x_i))}{\hat e(x_i)} - \frac{(1-d_i)(y_i-\hat\mu_0(x_i))}{1-\hat e(x_i)}\right]. \]

The nuisance functions are cross-fit ridge models.

2 Python API

Constructor: cm.AIPW

Call fit(y, d, x) with binary treatment d. summary() reports ate, se, vcov, and selected penalties for the outcome and propensity nuisance models.

print(inspect.signature(cm.AIPW))

(penalty=None, cv=5, n_folds=5, propensity_clip=0.02, seed=42)

cls = cm.AIPW
display(HTML(html_table(["Public method"], public_methods(cls))))

Public method
fit(self, /, y, d, x)
summary(self, /, vcov=None, lags=None, clusters=None)

3 Minimal example

rng=np.random.default_rng(14)
x=rng.normal(size=(420,3)); pi=1/(1+np.exp(-(.1+x@np.array([.6,-.3,.2])))); d=rng.binomial(1,pi,size=420).astype(float); y=.5+x@np.array([.2,-.1,.3])+1.0*d+rng.normal(size=420)
model=cm.AIPW(penalty=np.logspace(-4,1,10), cv=3, n_folds=4, seed=2); model.fit(y,d,x)
print(model.summary()["ate"])
print(model.summary()["se"])

1.1056887995229303
0.1055551427292932

4 summary() contract

The table below is generated by fitting the live class in this repository and then inspecting summary(). Shapes are shown because most values are plain NumPy arrays or scalars.

rng=np.random.default_rng(114); x=rng.normal(size=(160,3)); pi=1/(1+np.exp(-(.1+x@np.array([.6,-.3,.2])))); d=rng.binomial(1,pi,size=160).astype(float); y=.5+x@np.array([.2,-.1,.3])+d+rng.normal(size=160)
model=cm.AIPW(penalty=np.logspace(-4,1,6),cv=3,n_folds=4,seed=2); model.fit(y,d,x)
summary = model.summary()
display(HTML(html_table(["summary() key", "shape"], summary_shape_rows(summary))))

summary() key	shape
ate	()
se	()
vcov	(1, 1)
outcome0_penalties	(4,)
outcome1_penalties	(4,)
propensity_penalties	(4,)