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Local Distribution Estimators

This page documents local distribution treatment effect estimators that compute treatment effects weighted by treatment propensity within each stratum. These estimators are particularly useful for handling treatment assignment heterogeneity across strata and scenarios with imperfect compliance.

Local distribution treatment effects (LDTE) and local probability treatment effects (LPTE) provide methods for causal inference that account for treatment assignment vs. treatment receipt differences. For theoretical foundations on imperfect compliance scenarios, see:

  • Byambadalai, U., Hirata, T., Oka, T., & Yasui, S. (2025). Beyond the Average: Distributional Causal Inference under Imperfect Compliance. arXiv:2509.15594.

SimpleLocalDistributionEstimator

Bases: SimpleStratifiedDistributionEstimator

A class for computing Local Distribution Treatment Effects (LDTE) and Local Probability Treatment Effects (LPTE) using simple empirical estimation.

This estimator computes treatment effects that are weighted by treatment propensity within each stratum, providing estimates that are locally robust to treatment assignment heterogeneity across strata. It uses empirical methods without ML adjustment.

Initializes the SimpleLocalDistributionEstimator.

Returns: SimpleLocalDistributionEstimator: An instance of the estimator.

Source code in dte_adj/local.py 
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def __init__(self):
    """
    Initializes the SimpleLocalDistributionEstimator.

    Returns:
        SimpleLocalDistributionEstimator: An instance of the estimator.
    """
    super().__init__()

fit 

fit(
    covariates: ArrayLike,
    treatment_arms: ArrayLike,
    treatment_indicator: ArrayLike,
    outcomes: ArrayLike,
    strata: ArrayLike,
) -> SimpleLocalDistributionEstimator

Train the SimpleLocalDistributionEstimator.

Args: covariates: Pre-treatment covariates. treatment_arms: Treatment assignment variable (Z). treatment_indicator: Treatment indicator variable (D). outcomes: Scalar-valued observed outcome. strata: Stratum indicators.

Returns: SimpleLocalDistributionEstimator: The fitted estimator.

Source code in dte_adj/local.py 
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def fit(
    self,
    covariates: ArrayLike,
    treatment_arms: ArrayLike,
    treatment_indicator: ArrayLike,
    outcomes: ArrayLike,
    strata: ArrayLike,
) -> SimpleLocalDistributionEstimator:
    """
    Train the SimpleLocalDistributionEstimator.

    Args:
        covariates: Pre-treatment covariates.
        treatment_arms: Treatment assignment variable (Z).
        treatment_indicator: Treatment indicator variable (D).
        outcomes: Scalar-valued observed outcome.
        strata: Stratum indicators.

    Returns:
        SimpleLocalDistributionEstimator: The fitted estimator.
    """
    treatment_indicator = _convert_to_ndarray(treatment_indicator)
    super().fit(covariates, treatment_arms, outcomes, strata)
    self.treatment_indicator = treatment_indicator

    return self

predict_ldte 

predict_ldte(
    target_treatment_arm: int,
    control_treatment_arm: int,
    locations: Optional[ndarray] = None,
    alpha: float = 0.05,
    display_progress: bool = True,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray]

Compute Local Distribution Treatment Effects (LDTE).

LDTE measures the difference in cumulative distribution functions between treatment groups weighted by treatment propensity within each stratum. This provides estimates that are locally robust to treatment assignment heterogeneity across strata.

Args: target_treatment_arm (int): The index of the treatment arm of the treatment group. control_treatment_arm (int): The index of the treatment arm of the control group. locations (np.ndarray, optional): Scalar values to be used for computing the cumulative distribution. If None, evenly-spaced locations spanning the observed outcome range are generated automatically. The number of points is determined from data size and distribution via np.histogram_bin_edges(outcomes, bins='auto'). The actual array used is stored on self.last_locations. alpha (float, optional): Significance level of the confidence bound. Defaults to 0.05. display_progress (bool, optional): Whether to display a progress bar. Defaults to True.

Returns: Tuple[np.ndarray, np.ndarray, np.ndarray]: A tuple containing: - Expected LDTEs (np.ndarray): Local treatment effect estimates at each location - Lower bounds (np.ndarray): Lower confidence interval bounds - Upper bounds (np.ndarray): Upper confidence interval bounds

Example: 

import numpy as np
from sklearn.linear_model import LogisticRegression
from dte_adj import AdjustedLocalDistributionEstimator

# Generate sample data with strata
np.random.seed(42)
X = np.random.randn(1000, 5)
strata = np.random.choice([0, 1], size=1000)  # Binary strata
D = np.random.binomial(1, 0.3 + 0.4 * strata, 1000)  # Treatment depends on strata
Y = X[:, 0] + 2 * D + strata + np.random.randn(1000)

# Fit local estimator
base_model = LogisticRegression()
estimator = AdjustedLocalDistributionEstimator(base_model)
estimator.fit(X, D, D, Y, strata)  # treatment_arms = treatment_indicator for binary case

# Compute LDTE
locations = np.linspace(Y.min(), Y.max(), 20)
ldte, lower, upper = estimator.predict_ldte(
    target_treatment_arm=1,
    control_treatment_arm=0,
    locations=locations
)

print(f"LDTE shape: {ldte.shape}")  # Should match locations.shape
print(f"Average LDTE: {ldte.mean():.3f}")

Source code in dte_adj/local.py 
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def predict_ldte(
    self,
    target_treatment_arm: int,
    control_treatment_arm: int,
    locations: Optional[np.ndarray] = None,
    alpha: float = 0.05,
    display_progress: bool = True,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Compute Local Distribution Treatment Effects (LDTE).

    LDTE measures the difference in cumulative distribution functions between treatment groups
    weighted by treatment propensity within each stratum. This provides estimates that are
    locally robust to treatment assignment heterogeneity across strata.

    Args:
        target_treatment_arm (int): The index of the treatment arm of the treatment group.
        control_treatment_arm (int): The index of the treatment arm of the control group.
        locations (np.ndarray, optional): Scalar values to be used for computing the cumulative
            distribution. If None, evenly-spaced locations spanning the observed outcome range
            are generated automatically. The number of points is determined from data size and
            distribution via ``np.histogram_bin_edges(outcomes, bins='auto')``. The actual
            array used is stored on ``self.last_locations``.
        alpha (float, optional): Significance level of the confidence bound. Defaults to 0.05.
        display_progress (bool, optional): Whether to display a progress bar. Defaults to True.

    Returns:
        Tuple[np.ndarray, np.ndarray, np.ndarray]: A tuple containing:
            - Expected LDTEs (np.ndarray): Local treatment effect estimates at each location
            - Lower bounds (np.ndarray): Lower confidence interval bounds
            - Upper bounds (np.ndarray): Upper confidence interval bounds

    Example:
        ```python
        import numpy as np
        from sklearn.linear_model import LogisticRegression
        from dte_adj import AdjustedLocalDistributionEstimator

        # Generate sample data with strata
        np.random.seed(42)
        X = np.random.randn(1000, 5)
        strata = np.random.choice([0, 1], size=1000)  # Binary strata
        D = np.random.binomial(1, 0.3 + 0.4 * strata, 1000)  # Treatment depends on strata
        Y = X[:, 0] + 2 * D + strata + np.random.randn(1000)

        # Fit local estimator
        base_model = LogisticRegression()
        estimator = AdjustedLocalDistributionEstimator(base_model)
        estimator.fit(X, D, D, Y, strata)  # treatment_arms = treatment_indicator for binary case

        # Compute LDTE
        locations = np.linspace(Y.min(), Y.max(), 20)
        ldte, lower, upper = estimator.predict_ldte(
            target_treatment_arm=1,
            control_treatment_arm=0,
            locations=locations
        )

        print(f"LDTE shape: {ldte.shape}")  # Should match locations.shape
        print(f"Average LDTE: {ldte.mean():.3f}")
        ```
    """
    if locations is None:
        locations = _infer_default_locations(self.outcomes, for_intervals=False)
    self.last_locations = locations
    return compute_ldte(
        self,
        target_treatment_arm,
        control_treatment_arm,
        locations,
        alpha,
        display_progress,
    )

predict_lpte 

predict_lpte(
    target_treatment_arm: int,
    control_treatment_arm: int,
    locations: Optional[ndarray] = None,
    alpha: float = 0.05,
    display_progress: bool = True,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray]

Compute Local Probability Treatment Effects (LPTE).

LPTE measures the difference in probability mass between treatment groups for intervals defined by consecutive location pairs, weighted by treatment propensity within each stratum. This provides locally robust estimates of treatment effects on interval probabilities.

Args: target_treatment_arm (int): The index of the treatment arm of the treatment group. control_treatment_arm (int): The index of the treatment arm of the control group. locations (np.ndarray, optional): Scalar values defining interval boundaries for probability computation. For each interval (locations[i], locations[i+1]], the LPTE is computed. If None, boundaries spanning the observed outcome range are generated automatically with the left endpoint placed just below outcomes.min(). The number of boundaries is determined from data size and distribution via np.histogram_bin_edges(outcomes, bins='auto'). The actual array used is stored on self.last_locations. alpha (float, optional): Significance level of the confidence bound. Defaults to 0.05. display_progress (bool, optional): Whether to display a progress bar. Defaults to True.

Returns: Tuple[np.ndarray, np.ndarray, np.ndarray]: A tuple containing: - Expected LPTEs (np.ndarray): Local treatment effect estimates for each interval, shape (len(locations)-1,) - Lower bounds (np.ndarray): Lower confidence interval bounds - Upper bounds (np.ndarray): Upper confidence interval bounds

Example: 

import numpy as np
from dte_adj import SimpleLocalDistributionEstimator

# Generate sample data with strata
np.random.seed(42)
X = np.random.randn(1000, 5)
strata = np.random.choice([0, 1], size=1000)  # Binary strata
Z = np.random.binomial(1, 0.5, 1000)  # Treatment assignment
D = np.random.binomial(1, 0.3 + 0.4 * Z, 1000)  # Treatment receipt
Y = X[:, 0] + 2 * D + strata + np.random.randn(1000)

# Fit local estimator
estimator = SimpleLocalDistributionEstimator()
estimator.fit(X, Z, D, Y, strata)

# Define interval boundaries
locations = np.array([-2, -1, 0, 1, 2])  # Creates intervals: (-2,-1], (-1,0], (0,1], (1,2]

# Compute LPTE
lpte, lower, upper = estimator.predict_lpte(
    target_treatment_arm=1,
    control_treatment_arm=0,
    locations=locations
)

print(f"LPTE shape: {lpte.shape}")  # Should be (4,) for 4 intervals
print(f"Interval effects: {lpte}")

Source code in dte_adj/local.py 
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def predict_lpte(
    self,
    target_treatment_arm: int,
    control_treatment_arm: int,
    locations: Optional[np.ndarray] = None,
    alpha: float = 0.05,
    display_progress: bool = True,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Compute Local Probability Treatment Effects (LPTE).

    LPTE measures the difference in probability mass between treatment groups for intervals
    defined by consecutive location pairs, weighted by treatment propensity within each stratum.
    This provides locally robust estimates of treatment effects on interval probabilities.

    Args:
        target_treatment_arm (int): The index of the treatment arm of the treatment group.
        control_treatment_arm (int): The index of the treatment arm of the control group.
        locations (np.ndarray, optional): Scalar values defining interval boundaries for
            probability computation. For each interval (locations[i], locations[i+1]], the LPTE
            is computed. If None, boundaries spanning the observed outcome range are generated
            automatically with the left endpoint placed just below ``outcomes.min()``. The
            number of boundaries is determined from data size and distribution via
            ``np.histogram_bin_edges(outcomes, bins='auto')``. The actual array used is stored
            on ``self.last_locations``.
        alpha (float, optional): Significance level of the confidence bound. Defaults to 0.05.
        display_progress (bool, optional): Whether to display a progress bar. Defaults to True.

    Returns:
        Tuple[np.ndarray, np.ndarray, np.ndarray]: A tuple containing:
            - Expected LPTEs (np.ndarray): Local treatment effect estimates for each interval,
              shape (len(locations)-1,)
            - Lower bounds (np.ndarray): Lower confidence interval bounds
            - Upper bounds (np.ndarray): Upper confidence interval bounds

    Example:
        ```python
        import numpy as np
        from dte_adj import SimpleLocalDistributionEstimator

        # Generate sample data with strata
        np.random.seed(42)
        X = np.random.randn(1000, 5)
        strata = np.random.choice([0, 1], size=1000)  # Binary strata
        Z = np.random.binomial(1, 0.5, 1000)  # Treatment assignment
        D = np.random.binomial(1, 0.3 + 0.4 * Z, 1000)  # Treatment receipt
        Y = X[:, 0] + 2 * D + strata + np.random.randn(1000)

        # Fit local estimator
        estimator = SimpleLocalDistributionEstimator()
        estimator.fit(X, Z, D, Y, strata)

        # Define interval boundaries
        locations = np.array([-2, -1, 0, 1, 2])  # Creates intervals: (-2,-1], (-1,0], (0,1], (1,2]

        # Compute LPTE
        lpte, lower, upper = estimator.predict_lpte(
            target_treatment_arm=1,
            control_treatment_arm=0,
            locations=locations
        )

        print(f"LPTE shape: {lpte.shape}")  # Should be (4,) for 4 intervals
        print(f"Interval effects: {lpte}")
        ```
    """
    if locations is None:
        locations = _infer_default_locations(self.outcomes, for_intervals=True)
    self.last_locations = locations
    return compute_lpte(
        self,
        target_treatment_arm,
        control_treatment_arm,
        locations,
        alpha,
        display_progress,
    )

AdjustedLocalDistributionEstimator

Bases: AdjustedStratifiedDistributionEstimator

A class for computing Local Distribution Treatment Effects (LDTE) and Local Probability Treatment Effects (LPTE) using machine learning adjustment.

This estimator combines the benefits of ML adjustment with local treatment effect estimation, providing precise estimates of treatment effects that are weighted by treatment propensity within each stratum. It uses cross-fitting to avoid overfitting issues.

Source code in dte_adj/stratified.py 
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def __init__(self, base_model: Any, folds=3, is_multi_task=False):
    """
    Initializes the AdjustedDistributionEstimator.

    Args:
        base_model (scikit-learn estimator): The base model implementing used for conditional distribution function estimators. The model should implement fit(data, targets) and predict_proba(data).
        folds (int): The number of folds for cross-fitting.
        is_multi_task(bool): Whether to use multi-task learning. If True, your base model needs to support multi-task prediction (n_samples, n_features) -> (n_samples, n_targets).

    Returns:
        AdjustedDistributionEstimator: An instance of the estimator.
    """
    if (not hasattr(base_model, "predict")) and (
        not hasattr(base_model, "predict_proba")
    ):
        raise ValueError(
            "Base model should implement either predict_proba or predict"
        )
    self.base_model = base_model
    self.folds = folds
    self.is_multi_task = is_multi_task
    super().__init__()

fit 

fit(
    covariates: ArrayLike,
    treatment_arms: ArrayLike,
    treatment_indicator: ArrayLike,
    outcomes: ArrayLike,
    strata: ArrayLike,
) -> AdjustedLocalDistributionEstimator

Train the AdjustedLocalDistributionEstimator.

Args: covariates: Pre-treatment covariates. treatment_arms: Treatment assignment variable (Z). treatment_indicator: Treatment indicator variable (D). outcomes: Scalar-valued observed outcome. strata: Stratum indicators.

Returns: AdjustedLocalDistributionEstimator: The fitted estimator.

Source code in dte_adj/local.py 
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def fit(
    self,
    covariates: ArrayLike,
    treatment_arms: ArrayLike,
    treatment_indicator: ArrayLike,
    outcomes: ArrayLike,
    strata: ArrayLike,
) -> AdjustedLocalDistributionEstimator:
    """
    Train the AdjustedLocalDistributionEstimator.

    Args:
        covariates: Pre-treatment covariates.
        treatment_arms: Treatment assignment variable (Z).
        treatment_indicator: Treatment indicator variable (D).
        outcomes: Scalar-valued observed outcome.
        strata: Stratum indicators.

    Returns:
        AdjustedLocalDistributionEstimator: The fitted estimator.
    """
    treatment_indicator = _convert_to_ndarray(treatment_indicator)
    super().fit(covariates, treatment_arms, outcomes, strata)
    self.treatment_indicator = treatment_indicator

    return self

predict_ldte 

predict_ldte(
    target_treatment_arm: int,
    control_treatment_arm: int,
    locations: Optional[ndarray] = None,
    alpha: float = 0.05,
    display_progress: bool = True,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray]

Compute Local Distribution Treatment Effects (LDTE) using ML adjustment.

This method combines machine learning adjustment with local treatment effect estimation to provide precise, locally robust estimates of distributional treatment effects.

Args: target_treatment_arm (int): The index of the treatment arm of the treatment group. control_treatment_arm (int): The index of the treatment arm of the control group. locations (np.ndarray, optional): Scalar values to be used for computing the cumulative distribution. If None, evenly-spaced locations spanning the observed outcome range are generated automatically. The number of points is determined from data size and distribution via np.histogram_bin_edges(outcomes, bins='auto'). The actual array used is stored on self.last_locations. alpha (float, optional): Significance level of the confidence bound. Defaults to 0.05. display_progress (bool, optional): Whether to display a progress bar. Defaults to True.

Returns: Tuple[np.ndarray, np.ndarray, np.ndarray]: A tuple containing: - Expected LDTEs (np.ndarray): Local treatment effect estimates at each location - Lower bounds (np.ndarray): Lower confidence interval bounds - Upper bounds (np.ndarray): Upper confidence interval bounds

Example: 

import numpy as np
from sklearn.ensemble import RandomForestClassifier
from dte_adj import AdjustedLocalDistributionEstimator

# Generate confounded data with strata
np.random.seed(42)
X = np.random.randn(1000, 5)
strata = np.random.choice([0, 1], size=1000)
# Treatment assignment depends on covariates
Z_prob = 1 / (1 + np.exp(-(X[:, 0] + X[:, 1] + strata)))
Z = np.random.binomial(1, Z_prob, 1000)
D = np.random.binomial(1, 0.3 + 0.4 * Z, 1000)
Y = X.sum(axis=1) + 2 * D + strata + np.random.randn(1000)

# Fit adjusted local estimator
base_model = RandomForestClassifier(n_estimators=100)
estimator = AdjustedLocalDistributionEstimator(base_model, folds=3)
estimator.fit(X, Z, D, Y, strata)

# Compute LDTE with ML adjustment
locations = np.linspace(Y.min(), Y.max(), 20)
ldte, lower, upper = estimator.predict_ldte(
    target_treatment_arm=1,
    control_treatment_arm=0,
    locations=locations
)

print(f"Adjusted LDTE: {ldte.mean():.3f}")

Source code in dte_adj/local.py 
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def predict_ldte(
    self,
    target_treatment_arm: int,
    control_treatment_arm: int,
    locations: Optional[np.ndarray] = None,
    alpha: float = 0.05,
    display_progress: bool = True,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Compute Local Distribution Treatment Effects (LDTE) using ML adjustment.

    This method combines machine learning adjustment with local treatment effect estimation
    to provide precise, locally robust estimates of distributional treatment effects.

    Args:
        target_treatment_arm (int): The index of the treatment arm of the treatment group.
        control_treatment_arm (int): The index of the treatment arm of the control group.
        locations (np.ndarray, optional): Scalar values to be used for computing the cumulative
            distribution. If None, evenly-spaced locations spanning the observed outcome range
            are generated automatically. The number of points is determined from data size and
            distribution via ``np.histogram_bin_edges(outcomes, bins='auto')``. The actual
            array used is stored on ``self.last_locations``.
        alpha (float, optional): Significance level of the confidence bound. Defaults to 0.05.
        display_progress (bool, optional): Whether to display a progress bar. Defaults to True.

    Returns:
        Tuple[np.ndarray, np.ndarray, np.ndarray]: A tuple containing:
            - Expected LDTEs (np.ndarray): Local treatment effect estimates at each location
            - Lower bounds (np.ndarray): Lower confidence interval bounds
            - Upper bounds (np.ndarray): Upper confidence interval bounds

    Example:
        ```python
        import numpy as np
        from sklearn.ensemble import RandomForestClassifier
        from dte_adj import AdjustedLocalDistributionEstimator

        # Generate confounded data with strata
        np.random.seed(42)
        X = np.random.randn(1000, 5)
        strata = np.random.choice([0, 1], size=1000)
        # Treatment assignment depends on covariates
        Z_prob = 1 / (1 + np.exp(-(X[:, 0] + X[:, 1] + strata)))
        Z = np.random.binomial(1, Z_prob, 1000)
        D = np.random.binomial(1, 0.3 + 0.4 * Z, 1000)
        Y = X.sum(axis=1) + 2 * D + strata + np.random.randn(1000)

        # Fit adjusted local estimator
        base_model = RandomForestClassifier(n_estimators=100)
        estimator = AdjustedLocalDistributionEstimator(base_model, folds=3)
        estimator.fit(X, Z, D, Y, strata)

        # Compute LDTE with ML adjustment
        locations = np.linspace(Y.min(), Y.max(), 20)
        ldte, lower, upper = estimator.predict_ldte(
            target_treatment_arm=1,
            control_treatment_arm=0,
            locations=locations
        )

        print(f"Adjusted LDTE: {ldte.mean():.3f}")
        ```
    """
    if locations is None:
        locations = _infer_default_locations(self.outcomes, for_intervals=False)
    self.last_locations = locations
    return compute_ldte(
        self,
        target_treatment_arm,
        control_treatment_arm,
        locations,
        alpha,
        display_progress,
    )

predict_lpte 

predict_lpte(
    target_treatment_arm: int,
    control_treatment_arm: int,
    locations: Optional[ndarray] = None,
    alpha: float = 0.05,
    display_progress: bool = True,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray]

Compute Local Probability Treatment Effects (LPTE) using ML adjustment.

This method combines machine learning adjustment with local treatment effect estimation to provide precise estimates of treatment effects on interval probabilities.

Args: target_treatment_arm (int): The index of the treatment arm of the treatment group. control_treatment_arm (int): The index of the treatment arm of the control group. locations (np.ndarray, optional): Scalar values defining interval boundaries for probability computation. For each interval (locations[i], locations[i+1]], the LPTE is computed. If None, boundaries spanning the observed outcome range are generated automatically with the left endpoint placed just below outcomes.min(). The number of boundaries is determined from data size and distribution via np.histogram_bin_edges(outcomes, bins='auto'). The actual array used is stored on self.last_locations. alpha (float, optional): Significance level of the confidence bound. Defaults to 0.05. display_progress (bool, optional): Whether to display a progress bar. Defaults to True.

Returns: Tuple[np.ndarray, np.ndarray, np.ndarray]: A tuple containing: - Expected LPTEs (np.ndarray): Local treatment effect estimates for each interval, shape (len(locations)-1,) - Lower bounds (np.ndarray): Lower confidence interval bounds - Upper bounds (np.ndarray): Upper confidence interval bounds

Example: 

import numpy as np
from sklearn.linear_model import LogisticRegression
from dte_adj import AdjustedLocalDistributionEstimator

# Generate confounded data with strata
np.random.seed(42)
X = np.random.randn(1000, 5)
strata = np.random.choice([0, 1], size=1000)
# Treatment assignment depends on covariates
Z_prob = 1 / (1 + np.exp(-(X[:, 0] + strata)))
Z = np.random.binomial(1, Z_prob, 1000)
D = np.random.binomial(1, 0.3 + 0.4 * Z, 1000)
Y = X.sum(axis=1) + 2 * D + strata + np.random.randn(1000)

# Fit adjusted local estimator
base_model = LogisticRegression()
estimator = AdjustedLocalDistributionEstimator(base_model, folds=3)
estimator.fit(X, Z, D, Y, strata)

# Define interval boundaries
locations = np.array([-2, -1, 0, 1, 2])

# Compute LPTE with ML adjustment
lpte, lower, upper = estimator.predict_lpte(
    target_treatment_arm=1,
    control_treatment_arm=0,
    locations=locations
)

print(f"Adjusted LPTE: {lpte}")

Source code in dte_adj/local.py 
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def predict_lpte(
    self,
    target_treatment_arm: int,
    control_treatment_arm: int,
    locations: Optional[np.ndarray] = None,
    alpha: float = 0.05,
    display_progress: bool = True,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Compute Local Probability Treatment Effects (LPTE) using ML adjustment.

    This method combines machine learning adjustment with local treatment effect estimation
    to provide precise estimates of treatment effects on interval probabilities.

    Args:
        target_treatment_arm (int): The index of the treatment arm of the treatment group.
        control_treatment_arm (int): The index of the treatment arm of the control group.
        locations (np.ndarray, optional): Scalar values defining interval boundaries for
            probability computation. For each interval (locations[i], locations[i+1]], the LPTE
            is computed. If None, boundaries spanning the observed outcome range are generated
            automatically with the left endpoint placed just below ``outcomes.min()``. The
            number of boundaries is determined from data size and distribution via
            ``np.histogram_bin_edges(outcomes, bins='auto')``. The actual array used is stored
            on ``self.last_locations``.
        alpha (float, optional): Significance level of the confidence bound. Defaults to 0.05.
        display_progress (bool, optional): Whether to display a progress bar. Defaults to True.

    Returns:
        Tuple[np.ndarray, np.ndarray, np.ndarray]: A tuple containing:
            - Expected LPTEs (np.ndarray): Local treatment effect estimates for each interval,
              shape (len(locations)-1,)
            - Lower bounds (np.ndarray): Lower confidence interval bounds
            - Upper bounds (np.ndarray): Upper confidence interval bounds

    Example:
        ```python
        import numpy as np
        from sklearn.linear_model import LogisticRegression
        from dte_adj import AdjustedLocalDistributionEstimator

        # Generate confounded data with strata
        np.random.seed(42)
        X = np.random.randn(1000, 5)
        strata = np.random.choice([0, 1], size=1000)
        # Treatment assignment depends on covariates
        Z_prob = 1 / (1 + np.exp(-(X[:, 0] + strata)))
        Z = np.random.binomial(1, Z_prob, 1000)
        D = np.random.binomial(1, 0.3 + 0.4 * Z, 1000)
        Y = X.sum(axis=1) + 2 * D + strata + np.random.randn(1000)

        # Fit adjusted local estimator
        base_model = LogisticRegression()
        estimator = AdjustedLocalDistributionEstimator(base_model, folds=3)
        estimator.fit(X, Z, D, Y, strata)

        # Define interval boundaries
        locations = np.array([-2, -1, 0, 1, 2])

        # Compute LPTE with ML adjustment
        lpte, lower, upper = estimator.predict_lpte(
            target_treatment_arm=1,
            control_treatment_arm=0,
            locations=locations
        )

        print(f"Adjusted LPTE: {lpte}")
        ```
    """
    if locations is None:
        locations = _infer_default_locations(self.outcomes, for_intervals=True)
    self.last_locations = locations
    return compute_lpte(
        self,
        target_treatment_arm,
        control_treatment_arm,
        locations,
        alpha,
        display_progress,
    )