Attribute ate_ and method ate() give different results in CausalForestDML

Attribute ate_ and method ate() do not give the same point estimate and confidence interval. I suspect the former applies a doubly robust correction, whereas the latter may not.

Code to reproduce the issue:
import numpy as np
import pandas as pd
from econml.dml import CausalForestDML

# create synthetic data
n = 1000
np.random.seed(1)
T = np.random.randint(2, size=n)
X = np.random.normal(size=(n, 10))
W = np.random.normal(size=(n, 10))
Y = X**2 * T.reshape(-1, 1) + X * W
Y = np.sum(Y, axis=1)

# train model
m = CausalForestDML(discrete_treatment=True, max_features='sqrt', random_state=1)
m.tune(Y=Y, T=T, X=X, W=W)
m.fit(Y=Y, T=T, X=X, W=W)
m.summary()

# get ate (same as summary())
print(m.ate_)
print(m.ate_stderr_)

# get ate (not the same as summary())
print(m.ate(X=X, T0=0, T1=1))
print(m.ate_interval(X=X, T0=0, T1=1, alpha=.05))

The output is:

Especially, the confidence interval is substantially different.

The use case is to calculate the ATE for data not used for training.

Thanks!

Reproduce the discrepancy with the provided CausalForestDML example, then trace the implementations behind ate_, ate_stderr_, ate(), and ate_interval(). Compare behavior for the fitted data and held-out X, and identify the intended estimate and interval semantics. Done means the APIs agree or their documented differences are tested and clearly explained.