3. Local centering#

3.1. Method#

Local centering is a form of residualization and can improve the performance of forest estimators by regressing out the impact of the features on the outcome. Let us define the conditionally centered outcome \(\tilde{Y}_i\) as:

\[\tilde{Y}_i = Y_i - \hat{y}_{-i}(X_i)\]

where:

  • \(Y_i\) is the outcome for observation \(i\).

  • \(\hat{y}_{-i}(X_i)\) is an estimate of the conditional outcome expectation \(E[Y_i | X_i = x]\), given the realised \(x\) of the feature vector \(X_i\), and computed without using the observation \(i\).

3.2. Implementation#

Centered outcomes subtract fitted conditional means from observed outcomes. lc_estimator='RandomForest' is the default; other estimators and automatic selection are available. lc_yes=True enables centering.

With lc_cs_cv=True, construction-sample predictions are cross-fitted using lc_cs_cv_k folds. Filling and prediction observations use the fitted models. With lc_cs_cv=False, lc_cs_share reserves a separate sample for model fitting that is excluded from subsequent forest estimation.

Uncentered potential outcomes are expressed on the original outcome scale and can be used as policy scores. In the single-outcome example, their column names are available in results['iate_names_dic'][0]['names_y_pot_uncenter']. When efficiency improvements are enabled, the corresponding local centering models are used to restore the outcome levels.

See the API for estimator choices and resolved settings.

3.2.1. Example#

from mcf.example_data import example_data
from mcf.mcf_main import ModifiedCausalForest

# Generate example data using the built-in function `example_data()`
training_df, prediction_df, name_dict = example_data()


my_mcf = ModifiedCausalForest(
    var_y_name="outcome",
    var_d_name="treat",
    var_x_name_ord=["x_cont0", "x_cont1", "x_ord1"],
    # Activates local centering
    lc_yes = True,
    # Data for local centering & common support adjustment by crossvalidation
    lc_cs_cv = True,
    # Number of folds in cross-validation
    lc_cs_cv_k = 5
)

my_mcf.train(training_df)
results = my_mcf.predict(prediction_df)