Causal Stability Selection (CausalStabSel)

Stable effect modifier discovery with false discovery control

Associated paper

• Causal stability selection
  arXiv

Installation

pip install causalstabsel

Usage

from causalstabsel import causalstabsel

# load n-by-p feature matrix X, n-by-1 response vector y, and n-by-1 binary treatment indicator

# run causal stability selection
output = causalstabsel(X, y, treatment)

# select features based on target FDR
target_fdr = 0.1
q_values = output['q_values']
selected_features = [idx for idx, q_value in q_values.items() if q_value <= target_fdr]
print(f'Selected features (target FDR = {target_fdr}): {selected_features}')

Outputs

output = causalstabsel(X, y, treatment) is a dictionary containing:

• efp_scores: Dictionary whose keys are feature indices and values are their efp scores (dict of length p).
• q_values: Dictionary whose keys are feature indices and values are their q-values (dict of length p).
• runtime: Runtime of the algorithm in seconds (float).
• selected_features: Indices of features selected by CausalStabSel; empty list if target_fp and target_fdr are not specified (list of ints).
• stability_paths: Estimated selection probabilities at each parameter (array of shape (n_alphas, p)).

Selecting features

Each feature (column of X) is assigned:

• a q-value: the minimum false discovery rate (FDR) at which the feature is selected
• an efp score: the minimum expected number of false positives (E(FP)) at which the feature is selected

To select features:

• Control FDR by choosing all features with q_value ≤ target_fdr
  Example: Selecting features with q_value ≤ 0.1 controls the FDR at level 0.1
• Control E(FP) by choosing all features with efp_score ≤ target_fp
  Example: Selecting features with efp_score ≤ 2 controls the E(FP) at level 2

CATE estimators

cate_estimator: method used to estimate pseudo-outcomes (str; default 'drlearner_gb'):

• 'drlearner_gb', 'drlearner_rf', 'drlearner_ridge': Doubly-robust (DR) learner, with gradient boosting (XGBoost), random forest, or ridge regression nuisance models.
• 'tlearner_gb', 'tlearner_rf', 'tlearner_ridge': T-learner.
• 'xlearner_gb', 'xlearner_rf', 'xlearner_ridge': X-learner.
• 'causal_forest': Causal forest via econml's CausalForestDML. econml is not installed by default; install it with pip install causalstabsel[causal_forest].

cate_args: estimator-specific keyword arguments (dict; default None, which resolves to each estimator's own defaults).

propensity_estimator: how treatment propensities are estimated (used by the DR- and X-learners; default None, which assumes constant propensity of 0.5). Options:

• 'logistic_regression': Logistic regression (scikit-learn).
• 'rf': Random forest (scikit-learn).
• 'gb' or 'xgb': Gradient boosting (XGBoost).
• A float in [0, 1]: Use this constant propensity for all samples.
• Custom: a function propensity_estimator(x_train, t_train, x_test) -> array of propensities for x_test.

Smoothing

Cross-fit CATE estimates are noisy at the sample level, so by default causalstabsel smooths them with a secondary regression model before running the base selector:

• smooth_cate: Whether to smooth CATE pseudo-outcomes (bool; default None, which resolves to False if selector is 'l1'/'adaptive_lasso' and True otherwise).
• smoother: Regression model class used for smoothing when smooth_cate=True (default None, which resolves to xgb.XGBRegressor). Must implement .fit(X, y) / .predict(X).
• smoother_args: Arguments passed to smoother (dict; default None, which resolves to {'n_estimators': 20, 'max_depth': 3} for the default smoother).

Full list of causalstabsel arguments

Required arguments:

• X: Features (array of shape (n,p)), where n is the number of samples and p is the number of features.
• y: Response (array of shape (n,) or (n, 1)).
• treatment: Binary treatment indicator (array of shape (n,), values in {0, 1}).

Optional arguments:

• selector: Base algorithm used to score smoothed CATE estimates (str; default 'gb'). See the IPSS documentation for all options, including custom feature importance functions.
• selector_args: Arguments for the base algorithm (dict; default None).
• cate_estimator, cate_args, propensity_estimator: See CATE estimators above.
• smooth_cate, smoother, smoother_args: See Smoothing above.
• preselect: Preselect/filter features prior to subsampling (bool; default True).
• preselector, preselector_args: Preselection method and its arguments; see the IPSS documentation.
• target_fp: Target number of false positives to control (positive float; default None).
• target_fdr: Target false discovery rate (FDR) (positive float; default None).
• B: Number of subsampling steps (int; default 100).
• n_alphas: Number of values in the regularization or threshold grid (int; default None, resolves to an IPSS-determined default).
• ipss_function: Function applied to selection probabilities (str; default 'h3'). Options 'h1', 'h2', 'h3'; see IPSS.
• cutoff: Maximum value of the theoretical integral bound I(Lambda) (positive float; default 0.05).
• delta: Defines probability measure; see IPSS (float, list of floats, or None; default None resolves to 2). If a list, causalstabsel returns one result dictionary per value.
• subsample_size: Size of each subsample used for cross-fitting (int, float in (0, 1), or None; default None resolves to n // 2, and values above n // 2 are capped there since two disjoint subsamples of this size are drawn per step).
• standardize_X: Scale features to have mean 0, standard deviation 1 (bool; default None).
• center_y: Center response to have mean 0 (bool; default None).
• n_jobs: Number of jobs to run in parallel (int; default 1).