Question: How are the confidence intervals calculated in Single Tree Cate Interpreter?

I am using a Doubly Robust Forest Learning to calculate CATE for a single treatment variable and a set of X variables, and then fitting them to a tree to see the best criteria for splitting. The goal is to use a decision tree to identify the best features or rules for future heterogeneous studies. Currently we have over 15-20 features in X, but eventually we wish to identify the best combination of 3-5 features to select sub-population of maximum ROI. Hence, the motivation to calculate CATE for large number of X variables and then to back calculate ATE and other combinations of CATE. Hope this brief description of the objective makes sense.

As part of a few tests to better understand the package, I am aggregating the CATE estimates to obtain ATE, the standard error and the confidence interval (CI) associated with the ATE. I have found congruence between the ATE determined from the CATE estimates and that obtained using ate_inference function within EconML. (This is when the bug around the alpha in effect_inference came to our notice.)

Proceeding further, I wish to also verify the confidence intervals provided within the splits of the Single Tree Interpreter. However, I am noticing that the CI and CATE std within the trees do not agree with my calculations. In fact, the aggregated treatment effects agree with that obtained by taking the mean of CATE estimates within those splits. Hence, wondering how the CATE std and CI in tree are calculated?

Start with the Single Tree Interpreter behavior described in the issue, then compare its CATE standard deviation and confidence interval with the referenced ate_inference and effect_inference results. Done means the calculation and the discrepancy are clearly explained, with any needed documentation updates identified.