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Validation

Reusable model-validation workflows for train/test splits, cross-validation, and configurable learning curves. Use sparse multitask helpers when NaN target entries mean a property was not observed for a sample.

matgpr.validation

TrainTestValidationResult dataclass

Result from a single train/test validation run.

Attributes:

Name Type Description
model_name str

Human-readable model label used in reports.
fitted_estimator object

Estimator fitted on the training split.
metrics Mapping[str, float]

Flat dictionary with train/test regression metrics and, when available, uncertainty diagnostics.
predictions DataFrame

Prediction table with one row per train and test sample.
train_indices, test_indices

Integer sample positions used for the split.
Source code in matgpr/validation.py 
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@dataclass(frozen=True)
class TrainTestValidationResult:
    """Result from a single train/test validation run.

    Attributes
    ----------
    model_name
        Human-readable model label used in reports.
    fitted_estimator
        Estimator fitted on the training split.
    metrics
        Flat dictionary with train/test regression metrics and, when available,
        uncertainty diagnostics.
    predictions
        Prediction table with one row per train and test sample.
    train_indices, test_indices
        Integer sample positions used for the split.
    """

    model_name: str
    fitted_estimator: object
    metrics: Mapping[str, float]
    predictions: pd.DataFrame
    train_indices: np.ndarray
    test_indices: np.ndarray

    def metrics_frame(self) -> pd.DataFrame:
        """Return metrics as a one-row dataframe."""
        return pd.DataFrame([{**{"model": self.model_name}, **dict(self.metrics)}])

    @property
    def train_predictions(self) -> pd.DataFrame:
        """Predictions for training samples."""
        return self.predictions[self.predictions["split"] == "train"].reset_index(drop=True)

    @property
    def test_predictions(self) -> pd.DataFrame:
        """Predictions for held-out test samples."""
        return self.predictions[self.predictions["split"] == "test"].reset_index(drop=True)

train_predictions property

Predictions for training samples.

test_predictions property

Predictions for held-out test samples.

metrics_frame()

Return metrics as a one-row dataframe.

Source code in matgpr/validation.py 
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def metrics_frame(self) -> pd.DataFrame:
    """Return metrics as a one-row dataframe."""
    return pd.DataFrame([{**{"model": self.model_name}, **dict(self.metrics)}])

CoKrigingTrainTestValidationResult dataclass

Result from target-fidelity validation of a row-wise co-kriging model.

train_indices and test_indices refer only to rows at target_fidelity. fit_indices contains every row used to fit the estimator: all lower-fidelity rows plus the selected target-fidelity training rows.

Source code in matgpr/validation.py 
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@dataclass(frozen=True)
class CoKrigingTrainTestValidationResult:
    """Result from target-fidelity validation of a row-wise co-kriging model.

    ``train_indices`` and ``test_indices`` refer only to rows at
    ``target_fidelity``. ``fit_indices`` contains every row used to fit the
    estimator: all lower-fidelity rows plus the selected target-fidelity
    training rows.
    """

    model_name: str
    fitted_estimator: object
    metrics: Mapping[str, float]
    predictions: pd.DataFrame
    train_indices: np.ndarray
    test_indices: np.ndarray
    fit_indices: np.ndarray
    lower_fidelity_indices: np.ndarray
    target_fidelity: str
    low_fidelity: str
    rho: float | None = None

    def metrics_frame(self) -> pd.DataFrame:
        """Return metrics and validation protocol metadata as a one-row dataframe."""
        row = {
            "model": self.model_name,
            "target_fidelity": self.target_fidelity,
            "low_fidelity": self.low_fidelity,
            "n_fit": len(self.fit_indices),
            "n_target_train": len(self.train_indices),
            "n_target_test": len(self.test_indices),
            "n_lower_fidelity": len(self.lower_fidelity_indices),
        }
        if self.rho is not None:
            row["rho"] = self.rho
        row.update(dict(self.metrics))
        return pd.DataFrame([row])

    @property
    def train_predictions(self) -> pd.DataFrame:
        """Target-fidelity predictions for training samples."""
        return self.predictions[self.predictions["split"] == "train"].reset_index(drop=True)

    @property
    def test_predictions(self) -> pd.DataFrame:
        """Target-fidelity predictions for held-out test samples."""
        return self.predictions[self.predictions["split"] == "test"].reset_index(drop=True)

train_predictions property

Target-fidelity predictions for training samples.

test_predictions property

Target-fidelity predictions for held-out test samples.

metrics_frame()

Return metrics and validation protocol metadata as a one-row dataframe.

Source code in matgpr/validation.py 
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def metrics_frame(self) -> pd.DataFrame:
    """Return metrics and validation protocol metadata as a one-row dataframe."""
    row = {
        "model": self.model_name,
        "target_fidelity": self.target_fidelity,
        "low_fidelity": self.low_fidelity,
        "n_fit": len(self.fit_indices),
        "n_target_train": len(self.train_indices),
        "n_target_test": len(self.test_indices),
        "n_lower_fidelity": len(self.lower_fidelity_indices),
    }
    if self.rho is not None:
        row["rho"] = self.rho
    row.update(dict(self.metrics))
    return pd.DataFrame([row])

CrossValidationResult dataclass

Result from k-fold or splitter-based cross-validation.

Source code in matgpr/validation.py 
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@dataclass(frozen=True)
class CrossValidationResult:
    """Result from k-fold or splitter-based cross-validation."""

    model_name: str
    fold_metrics: pd.DataFrame
    predictions: pd.DataFrame

    def summary(self, metric_columns: Sequence[str] | None = None) -> pd.DataFrame:
        """Summarize fold metrics with mean, standard deviation, min, and max."""
        return _summarize_metrics(
            self.fold_metrics, group_by=("model",), metric_columns=metric_columns
        )

summary(metric_columns=None)

Summarize fold metrics with mean, standard deviation, min, and max.

Source code in matgpr/validation.py 
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def summary(self, metric_columns: Sequence[str] | None = None) -> pd.DataFrame:
    """Summarize fold metrics with mean, standard deviation, min, and max."""
    return _summarize_metrics(
        self.fold_metrics, group_by=("model",), metric_columns=metric_columns
    )

LearningCurveResult dataclass

Result from learning-curve evaluation across train-set sizes.

Source code in matgpr/validation.py 
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@dataclass(frozen=True)
class LearningCurveResult:
    """Result from learning-curve evaluation across train-set sizes."""

    model_name: str
    runs: pd.DataFrame
    predictions: pd.DataFrame | None = None
    metric_names: Sequence[str] = ("RMSE", "R2", "MAE", "r")
    metric_splits: Sequence[str] = ("test",)

    def summary(
        self,
        metric_columns: Sequence[str] | None = None,
        *,
        metrics: Sequence[str] | str | None = None,
        splits: Sequence[str] | str | None = None,
    ) -> pd.DataFrame:
        """Summarize repeated runs by model and train-set size."""
        if metric_columns is None:
            metric_columns = _metric_columns(
                self.runs,
                metrics=self.metric_names if metrics is None else metrics,
                splits=self.metric_splits if splits is None else splits,
            )
        return _summarize_metrics(
            self.runs,
            group_by=("model", "train_size", "train_size_percent", "n_train"),
            metric_columns=metric_columns,
        )

summary(metric_columns=None, *, metrics=None, splits=None)

Summarize repeated runs by model and train-set size.

Source code in matgpr/validation.py 
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def summary(
    self,
    metric_columns: Sequence[str] | None = None,
    *,
    metrics: Sequence[str] | str | None = None,
    splits: Sequence[str] | str | None = None,
) -> pd.DataFrame:
    """Summarize repeated runs by model and train-set size."""
    if metric_columns is None:
        metric_columns = _metric_columns(
            self.runs,
            metrics=self.metric_names if metrics is None else metrics,
            splits=self.metric_splits if splits is None else splits,
        )
    return _summarize_metrics(
        self.runs,
        group_by=("model", "train_size", "train_size_percent", "n_train"),
        metric_columns=metric_columns,
    )

MultitaskTrainTestValidationResult dataclass

Result from a multitask train/test validation run.

Attributes:

Name Type Description
model_name str

Human-readable model label used in reports.
fitted_estimator object

Estimator fitted on the training split.
task_metrics DataFrame

Per-task metrics with one row per split and task.
predictions DataFrame

Long-form prediction table with one row per sample, split, and task.
train_indices, test_indices

Integer sample positions used for the split.
Source code in matgpr/validation.py 
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@dataclass(frozen=True)
class MultitaskTrainTestValidationResult:
    """Result from a multitask train/test validation run.

    Attributes
    ----------
    model_name
        Human-readable model label used in reports.
    fitted_estimator
        Estimator fitted on the training split.
    task_metrics
        Per-task metrics with one row per split and task.
    predictions
        Long-form prediction table with one row per sample, split, and task.
    train_indices, test_indices
        Integer sample positions used for the split.
    """

    model_name: str
    fitted_estimator: object
    task_metrics: pd.DataFrame
    predictions: pd.DataFrame
    train_indices: np.ndarray
    test_indices: np.ndarray

    def metrics_frame(self) -> pd.DataFrame:
        """Return the per-task metrics dataframe."""
        return self.task_metrics.copy()

    def summary(
        self,
        metric_columns: Sequence[str] | None = None,
        *,
        group_by: Sequence[str] = ("model", "split"),
    ) -> pd.DataFrame:
        """Summarize per-task metrics across tasks for each split."""
        return _summarize_metrics(
            self.task_metrics,
            group_by=group_by,
            metric_columns=metric_columns,
        )

    @property
    def train_predictions(self) -> pd.DataFrame:
        """Predictions for training samples."""
        return self.predictions[self.predictions["split"] == "train"].reset_index(drop=True)

    @property
    def test_predictions(self) -> pd.DataFrame:
        """Predictions for held-out test samples."""
        return self.predictions[self.predictions["split"] == "test"].reset_index(drop=True)

train_predictions property

Predictions for training samples.

test_predictions property

Predictions for held-out test samples.

metrics_frame()

Return the per-task metrics dataframe.

Source code in matgpr/validation.py 
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def metrics_frame(self) -> pd.DataFrame:
    """Return the per-task metrics dataframe."""
    return self.task_metrics.copy()

summary(metric_columns=None, *, group_by=('model', 'split'))

Summarize per-task metrics across tasks for each split.

Source code in matgpr/validation.py 
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def summary(
    self,
    metric_columns: Sequence[str] | None = None,
    *,
    group_by: Sequence[str] = ("model", "split"),
) -> pd.DataFrame:
    """Summarize per-task metrics across tasks for each split."""
    return _summarize_metrics(
        self.task_metrics,
        group_by=group_by,
        metric_columns=metric_columns,
    )

SparseMultitaskTrainTestValidationResult dataclass

Result from a sparse multitask train/test validation run.

The prediction table keeps one row per sample and task, including entries where the target was unobserved. Use observed_predictions for parity-plot-ready rows with finite ground-truth values.

Source code in matgpr/validation.py 
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@dataclass(frozen=True)
class SparseMultitaskTrainTestValidationResult:
    """Result from a sparse multitask train/test validation run.

    The prediction table keeps one row per sample and task, including entries
    where the target was unobserved. Use ``observed_predictions`` for
    parity-plot-ready rows with finite ground-truth values.
    """

    model_name: str
    fitted_estimator: object
    task_metrics: pd.DataFrame
    predictions: pd.DataFrame
    train_indices: np.ndarray
    test_indices: np.ndarray

    def metrics_frame(self) -> pd.DataFrame:
        """Return the per-task sparse metrics dataframe."""
        return self.task_metrics.copy()

    def summary(
        self,
        metric_columns: Sequence[str] | None = None,
        *,
        group_by: Sequence[str] = ("model", "split"),
    ) -> pd.DataFrame:
        """Summarize sparse per-task metrics across tasks for each split."""
        return _summarize_metrics(
            self.task_metrics,
            group_by=group_by,
            metric_columns=metric_columns,
        )

    @property
    def train_predictions(self) -> pd.DataFrame:
        """Predictions for training samples."""
        return self.predictions[self.predictions["split"] == "train"].reset_index(drop=True)

    @property
    def test_predictions(self) -> pd.DataFrame:
        """Predictions for held-out test samples."""
        return self.predictions[self.predictions["split"] == "test"].reset_index(drop=True)

    @property
    def observed_predictions(self) -> pd.DataFrame:
        """Prediction rows whose target values are observed."""
        return self.predictions[self.predictions["observed"]].reset_index(drop=True)

train_predictions property

Predictions for training samples.

test_predictions property

Predictions for held-out test samples.

observed_predictions property

Prediction rows whose target values are observed.

metrics_frame()

Return the per-task sparse metrics dataframe.

Source code in matgpr/validation.py 
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def metrics_frame(self) -> pd.DataFrame:
    """Return the per-task sparse metrics dataframe."""
    return self.task_metrics.copy()

summary(metric_columns=None, *, group_by=('model', 'split'))

Summarize sparse per-task metrics across tasks for each split.

Source code in matgpr/validation.py 
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def summary(
    self,
    metric_columns: Sequence[str] | None = None,
    *,
    group_by: Sequence[str] = ("model", "split"),
) -> pd.DataFrame:
    """Summarize sparse per-task metrics across tasks for each split."""
    return _summarize_metrics(
        self.task_metrics,
        group_by=group_by,
        metric_columns=metric_columns,
    )

evaluate_train_test_split(estimator, X, y, *, train_indices=None, test_indices=None, test_size=0.2, train_size=None, random_state=None, shuffle=True, model_name=None, return_std=True, confidence_level=0.95, include_observation_noise=None, fit_params=None)

Fit an estimator on one train/test split and return report-ready outputs.

This is the reusable package equivalent of the validation block commonly repeated in notebooks: split, fit, predict train/test values, calculate metrics, and store a parity-plot-ready prediction table.

Source code in matgpr/validation.py 
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def evaluate_train_test_split(
    estimator,
    X,
    y,
    *,
    train_indices: Sequence[int] | None = None,
    test_indices: Sequence[int] | None = None,
    test_size: float | int = 0.2,
    train_size: float | int | None = None,
    random_state: int | None = None,
    shuffle: bool = True,
    model_name: str | None = None,
    return_std: bool = True,
    confidence_level: float = 0.95,
    include_observation_noise: bool | None = None,
    fit_params: Mapping[str, object] | None = None,
) -> TrainTestValidationResult:
    """Fit an estimator on one train/test split and return report-ready outputs.

    This is the reusable package equivalent of the validation block commonly
    repeated in notebooks: split, fit, predict train/test values, calculate
    metrics, and store a parity-plot-ready prediction table.
    """
    n_samples = _validate_xy_length(X, y)
    labels = _sample_labels(y, n_samples)

    if train_indices is None and test_indices is None:
        train_indices, test_indices = train_test_split(
            np.arange(n_samples),
            train_size=train_size,
            test_size=test_size,
            random_state=random_state,
            shuffle=shuffle,
        )
    elif train_indices is None or test_indices is None:
        raise ValueError("train_indices and test_indices must be supplied together")
    else:
        train_indices = _to_index_array(train_indices, "train_indices", n_samples)
        test_indices = _to_index_array(test_indices, "test_indices", n_samples)

    result = _fit_evaluate_indices(
        estimator,
        X,
        y,
        train_indices=np.asarray(train_indices, dtype=int),
        test_indices=np.asarray(test_indices, dtype=int),
        labels=labels,
        model_name=model_name or _estimator_name(estimator),
        return_std=return_std,
        confidence_level=confidence_level,
        include_observation_noise=include_observation_noise,
        fit_params=fit_params,
        random_state=random_state,
        context={},
    )
    return TrainTestValidationResult(
        model_name=result["model_name"],
        fitted_estimator=result["estimator"],
        metrics=result["metrics"],
        predictions=result["predictions"],
        train_indices=np.asarray(train_indices, dtype=int),
        test_indices=np.asarray(test_indices, dtype=int),
    )

evaluate_cokriging_train_test_split(estimator, X, y, fidelity, *, target_fidelity=None, low_fidelity=None, fidelity_order=None, sample_id=None, train_indices=None, test_indices=None, test_size=0.2, train_size=None, random_state=None, shuffle=True, model_name=None, return_std=True, confidence_level=0.95, include_observation_noise=None, fit_params=None)

Validate a two-level co-kriging estimator on target-fidelity rows.

The split is performed only among rows labeled target_fidelity. All lower-fidelity rows are retained for fitting in every split, which matches the usual low-data protocol for simulation-plus-experiment materials datasets. The returned prediction table is parity-plot-ready and preserves co-kriging component columns such as scaled_low_fidelity_pred and discrepancy_pred when the estimator exposes them.

Source code in matgpr/validation.py 
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def evaluate_cokriging_train_test_split(
    estimator,
    X,
    y,
    fidelity,
    *,
    target_fidelity: str | None = None,
    low_fidelity: str | None = None,
    fidelity_order: Sequence[str] | None = None,
    sample_id=None,
    train_indices: Sequence[int] | None = None,
    test_indices: Sequence[int] | None = None,
    test_size: float | int = 0.2,
    train_size: float | int | None = None,
    random_state: int | None = None,
    shuffle: bool = True,
    model_name: str | None = None,
    return_std: bool = True,
    confidence_level: float = 0.95,
    include_observation_noise: bool | None = None,
    fit_params: Mapping[str, object] | None = None,
) -> CoKrigingTrainTestValidationResult:
    """Validate a two-level co-kriging estimator on target-fidelity rows.

    The split is performed only among rows labeled ``target_fidelity``. All
    lower-fidelity rows are retained for fitting in every split, which matches
    the usual low-data protocol for simulation-plus-experiment materials
    datasets. The returned prediction table is parity-plot-ready and preserves
    co-kriging component columns such as ``scaled_low_fidelity_pred`` and
    ``discrepancy_pred`` when the estimator exposes them.
    """
    n_samples = _validate_xy_length(X, y)
    labels = _sample_labels(y, n_samples)
    fidelity_labels = _to_fidelity_label_array(fidelity, n_samples=n_samples)
    sample_id_array = _resolve_optional_row_values(sample_id, n_samples=n_samples, name="sample_id")
    fidelity_names, target_name, low_name = _resolve_cokriging_validation_levels(
        fidelity_labels,
        estimator=estimator,
        target_fidelity=target_fidelity,
        low_fidelity=low_fidelity,
        fidelity_order=fidelity_order,
    )

    target_mask = fidelity_labels == target_name
    target_positions = np.flatnonzero(target_mask)
    if target_positions.size < 2:
        raise ValueError("At least two target-fidelity rows are required for validation")

    if train_indices is None and test_indices is None:
        train_indices, test_indices = train_test_split(
            target_positions,
            train_size=train_size,
            test_size=test_size,
            random_state=random_state,
            shuffle=shuffle,
        )
    elif train_indices is None or test_indices is None:
        raise ValueError("train_indices and test_indices must be supplied together")
    else:
        train_indices = _to_index_array(train_indices, "train_indices", n_samples)
        test_indices = _to_index_array(test_indices, "test_indices", n_samples)

    train_indices = np.asarray(train_indices, dtype=int)
    test_indices = np.asarray(test_indices, dtype=int)
    _validate_split_indices(train_indices, test_indices, n_samples)
    _validate_target_fidelity_indices(
        train_indices,
        target_mask=target_mask,
        name="train_indices",
        target_fidelity=target_name,
    )
    _validate_target_fidelity_indices(
        test_indices,
        target_mask=target_mask,
        name="test_indices",
        target_fidelity=target_name,
    )

    fit_indices, lower_fidelity_indices = _cokriging_fit_indices(
        fidelity_labels,
        target_fidelity=target_name,
        train_indices=train_indices,
    )

    result = _fit_evaluate_cokriging_indices(
        estimator,
        X,
        y,
        fidelity_labels=fidelity_labels,
        sample_id=sample_id_array,
        fit_indices=fit_indices,
        train_indices=train_indices,
        test_indices=test_indices,
        labels=labels,
        fidelity_names=fidelity_names,
        target_fidelity=target_name,
        low_fidelity=low_name,
        model_name=model_name or _estimator_name(estimator),
        return_std=return_std,
        confidence_level=confidence_level,
        include_observation_noise=include_observation_noise,
        fit_params=fit_params,
        random_state=random_state,
        context={
            "target_fidelity": target_name,
            "low_fidelity": low_name,
            "n_lower_fidelity": len(lower_fidelity_indices),
        },
    )

    return CoKrigingTrainTestValidationResult(
        model_name=result["model_name"],
        fitted_estimator=result["estimator"],
        metrics=result["metrics"],
        predictions=result["predictions"],
        train_indices=train_indices,
        test_indices=test_indices,
        fit_indices=fit_indices,
        lower_fidelity_indices=lower_fidelity_indices,
        target_fidelity=target_name,
        low_fidelity=low_name,
        rho=result["rho"],
    )

summarize_multitask_predictions(y_true, y_pred, y_std=None, *, task_names=None, model_name='model', split='test', confidence_level=0.95)

Return per-task regression and uncertainty metrics.

Parameters:

Name Type Description Default
y_true

True target matrix with shape (n_samples, n_tasks). Dataframes are accepted; their columns are used as task names when task_names is not supplied.

 required
y_pred

Predicted target matrix with the same shape as y_true. Objects with mean, std, and task_names attributes, such as :class:matgpr.MultitaskGPyTorchPrediction, are also accepted.

 required
y_std

Optional predictive standard deviations with the same shape as y_true. If omitted and y_pred has a std attribute, that attribute is used.

 None
task_names Sequence[str] | None

Optional task names in target-column order.

 None
model_name str

Labels stored in the returned dataframe for report tables.

 'model'
split str

Labels stored in the returned dataframe for report tables.

 'model'
confidence_level float

Gaussian interval level used for uncertainty coverage diagnostics.

 0.95

Returns:

Type Description
DataFrame

One row per task with RMSE, MAE, R2, Pearson r, sample count, and uncertainty diagnostics when predictive standard deviations are available.
Source code in matgpr/validation.py 
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def summarize_multitask_predictions(
    y_true,
    y_pred,
    y_std=None,
    *,
    task_names: Sequence[str] | None = None,
    model_name: str = "model",
    split: str = "test",
    confidence_level: float = 0.95,
) -> pd.DataFrame:
    """Return per-task regression and uncertainty metrics.

    Parameters
    ----------
    y_true
        True target matrix with shape ``(n_samples, n_tasks)``. Dataframes are
        accepted; their columns are used as task names when ``task_names`` is
        not supplied.
    y_pred
        Predicted target matrix with the same shape as ``y_true``. Objects with
        ``mean``, ``std``, and ``task_names`` attributes, such as
        :class:`matgpr.MultitaskGPyTorchPrediction`, are also accepted.
    y_std
        Optional predictive standard deviations with the same shape as
        ``y_true``. If omitted and ``y_pred`` has a ``std`` attribute, that
        attribute is used.
    task_names
        Optional task names in target-column order.
    model_name, split
        Labels stored in the returned dataframe for report tables.
    confidence_level
        Gaussian interval level used for uncertainty coverage diagnostics.

    Returns
    -------
    pandas.DataFrame
        One row per task with RMSE, MAE, R2, Pearson ``r``, sample count, and
        uncertainty diagnostics when predictive standard deviations are
        available.
    """
    prediction_task_names = getattr(y_pred, "task_names", None)
    if y_std is None and _is_prediction_container(y_pred) and hasattr(y_pred, "std"):
        y_std = getattr(y_pred, "std")
    if _is_prediction_container(y_pred):
        y_pred = getattr(y_pred, "mean")

    y_true_array = _to_2d_float(y_true, "y_true")
    y_pred_array = _to_2d_float(y_pred, "y_pred")
    _validate_same_2d_shape(y_true_array, y_pred_array, "y_true", "y_pred")
    y_std_array = _to_optional_2d_std(y_std) if y_std is not None else None
    if y_std_array is not None:
        _validate_same_2d_shape(y_true_array, y_std_array, "y_true", "y_std")

    resolved_task_names = _resolve_multitask_names(
        task_names=task_names,
        n_tasks=y_true_array.shape[1],
        y=y_true,
        prediction_task_names=prediction_task_names,
    )
    rows = []
    for task_index, task_name in enumerate(resolved_task_names):
        metrics = regression_metrics(
            y_true_array[:, task_index],
            y_pred_array[:, task_index],
        )
        row = {
            "model": str(model_name),
            "split": str(split),
            "task": task_name,
            "task_index": task_index,
            "n_samples": y_true_array.shape[0],
            **metrics,
        }
        if y_std_array is not None:
            row.update(
                uncertainty_diagnostics(
                    y_true_array[:, task_index],
                    y_pred_array[:, task_index],
                    y_std_array[:, task_index],
                    confidence_level=confidence_level,
                )
            )
        rows.append(row)
    return pd.DataFrame(rows)

summarize_sparse_multitask_predictions(y_true, y_pred, y_std=None, *, task_names=None, model_name='model', split='test', confidence_level=0.95)

Return per-task metrics for sparse multitask targets.

NaN values in y_true are treated as unobserved task entries and are ignored for regression and uncertainty metrics. The returned dataframe keeps the total row count, observed count, and missing fraction for each task so sparse validation protocols are transparent in reports.

Source code in matgpr/validation.py 
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def summarize_sparse_multitask_predictions(
    y_true,
    y_pred,
    y_std=None,
    *,
    task_names: Sequence[str] | None = None,
    model_name: str = "model",
    split: str = "test",
    confidence_level: float = 0.95,
) -> pd.DataFrame:
    """Return per-task metrics for sparse multitask targets.

    ``NaN`` values in ``y_true`` are treated as unobserved task entries and are
    ignored for regression and uncertainty metrics. The returned dataframe
    keeps the total row count, observed count, and missing fraction for each
    task so sparse validation protocols are transparent in reports.
    """
    prediction_task_names = getattr(y_pred, "task_names", None)
    if y_std is None and _is_prediction_container(y_pred) and hasattr(y_pred, "std"):
        y_std = getattr(y_pred, "std")
    if _is_prediction_container(y_pred):
        y_pred = getattr(y_pred, "mean")

    y_true_array = _to_2d_float_allow_nan(y_true, "y_true")
    y_pred_array = _to_2d_float(y_pred, "y_pred")
    _validate_same_2d_shape(y_true_array, y_pred_array, "y_true", "y_pred")
    y_std_array = _to_optional_2d_std(y_std) if y_std is not None else None
    if y_std_array is not None:
        _validate_same_2d_shape(y_true_array, y_std_array, "y_true", "y_std")

    resolved_task_names = _resolve_multitask_names(
        task_names=task_names,
        n_tasks=y_true_array.shape[1],
        y=y_true,
        prediction_task_names=prediction_task_names,
    )
    rows = []
    n_samples = y_true_array.shape[0]
    for task_index, task_name in enumerate(resolved_task_names):
        observed_mask = np.isfinite(y_true_array[:, task_index])
        n_observed = int(observed_mask.sum())
        n_missing = int(n_samples - n_observed)
        metrics = _observed_regression_metrics(
            y_true_array[observed_mask, task_index],
            y_pred_array[observed_mask, task_index],
        )
        row = {
            "model": str(model_name),
            "split": str(split),
            "task": task_name,
            "task_index": task_index,
            "n_samples": n_samples,
            "n_observed": n_observed,
            "n_missing": n_missing,
            "observed_fraction": n_observed / n_samples,
            "missing_fraction": n_missing / n_samples,
            **metrics,
        }
        if y_std_array is not None:
            if n_observed:
                row.update(
                    uncertainty_diagnostics(
                        y_true_array[observed_mask, task_index],
                        y_pred_array[observed_mask, task_index],
                        y_std_array[observed_mask, task_index],
                        confidence_level=confidence_level,
                    )
                )
            else:
                row.update(_empty_uncertainty_diagnostics(confidence_level))
        rows.append(row)
    return pd.DataFrame(rows)

evaluate_multitask_train_test_split(estimator, X, y, *, train_indices=None, test_indices=None, test_size=0.2, train_size=None, random_state=None, shuffle=True, model_name=None, task_names=None, return_std=True, confidence_level=0.95, include_observation_noise=None, fit_params=None)

Fit a multitask estimator on one split and return per-task summaries.

This is the multitask counterpart of :func:evaluate_train_test_split. It keeps validation outputs in report-ready form: per-task metrics for the train and held-out test splits plus a long-form parity-plot table with predictive uncertainty when the estimator provides it.

Source code in matgpr/validation.py 
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def evaluate_multitask_train_test_split(
    estimator,
    X,
    y,
    *,
    train_indices: Sequence[int] | None = None,
    test_indices: Sequence[int] | None = None,
    test_size: float | int = 0.2,
    train_size: float | int | None = None,
    random_state: int | None = None,
    shuffle: bool = True,
    model_name: str | None = None,
    task_names: Sequence[str] | None = None,
    return_std: bool = True,
    confidence_level: float = 0.95,
    include_observation_noise: bool | None = None,
    fit_params: Mapping[str, object] | None = None,
) -> MultitaskTrainTestValidationResult:
    """Fit a multitask estimator on one split and return per-task summaries.

    This is the multitask counterpart of :func:`evaluate_train_test_split`.
    It keeps validation outputs in report-ready form: per-task metrics for the
    train and held-out test splits plus a long-form parity-plot table with
    predictive uncertainty when the estimator provides it.
    """
    n_samples, _ = _validate_multitask_xy_length(X, y)
    labels = _sample_labels(y, n_samples)

    if train_indices is None and test_indices is None:
        train_indices, test_indices = train_test_split(
            np.arange(n_samples),
            train_size=train_size,
            test_size=test_size,
            random_state=random_state,
            shuffle=shuffle,
        )
    elif train_indices is None or test_indices is None:
        raise ValueError("train_indices and test_indices must be supplied together")
    else:
        train_indices = _to_index_array(train_indices, "train_indices", n_samples)
        test_indices = _to_index_array(test_indices, "test_indices", n_samples)

    train_indices = np.asarray(train_indices, dtype=int)
    test_indices = np.asarray(test_indices, dtype=int)
    _validate_split_indices(train_indices, test_indices, n_samples)

    fitted_estimator = _clone_estimator(estimator, random_state=random_state)
    X_train = _safe_index(X, train_indices)
    X_test = _safe_index(X, test_indices)
    y_train = _safe_index(y, train_indices)
    y_test = _safe_index(y, test_indices)
    model_name = model_name or _estimator_name(estimator)

    fitted_estimator.fit(X_train, y_train, **dict(fit_params or {}))
    y_train_pred, y_train_std, train_prediction_task_names = _predict_multitask_estimator(
        fitted_estimator,
        X_train,
        return_std=return_std,
        confidence_level=confidence_level,
        include_observation_noise=include_observation_noise,
    )
    y_test_pred, y_test_std, test_prediction_task_names = _predict_multitask_estimator(
        fitted_estimator,
        X_test,
        return_std=return_std,
        confidence_level=confidence_level,
        include_observation_noise=include_observation_noise,
    )
    fitted_task_names = getattr(fitted_estimator, "task_names_", None)
    resolved_task_names = _resolve_multitask_names(
        task_names=task_names,
        n_tasks=_to_2d_float(y_train, "y_train").shape[1],
        y=y,
        prediction_task_names=_first_available_task_names(
            fitted_task_names,
            train_prediction_task_names,
            test_prediction_task_names,
        ),
    )

    train_metrics = summarize_multitask_predictions(
        y_train,
        y_train_pred,
        y_train_std,
        task_names=resolved_task_names,
        model_name=model_name,
        split="train",
        confidence_level=confidence_level,
    )
    test_metrics = summarize_multitask_predictions(
        y_test,
        y_test_pred,
        y_test_std,
        task_names=resolved_task_names,
        model_name=model_name,
        split="test",
        confidence_level=confidence_level,
    )
    predictions = pd.concat(
        [
            _multitask_prediction_frame(
                model_name,
                "train",
                train_indices,
                labels,
                y_train,
                y_train_pred,
                y_train_std,
                task_names=resolved_task_names,
                confidence_level=confidence_level,
            ),
            _multitask_prediction_frame(
                model_name,
                "test",
                test_indices,
                labels,
                y_test,
                y_test_pred,
                y_test_std,
                task_names=resolved_task_names,
                confidence_level=confidence_level,
            ),
        ],
        ignore_index=True,
    )
    return MultitaskTrainTestValidationResult(
        model_name=model_name,
        fitted_estimator=fitted_estimator,
        task_metrics=pd.concat([train_metrics, test_metrics], ignore_index=True),
        predictions=predictions,
        train_indices=train_indices,
        test_indices=test_indices,
    )

evaluate_sparse_multitask_train_test_split(estimator, X, y, *, train_indices=None, test_indices=None, test_size=0.2, train_size=None, random_state=None, shuffle=True, model_name=None, task_names=None, return_std=True, confidence_level=0.95, include_observation_noise=None, fit_params=None)

Fit a sparse multitask estimator and evaluate observed target entries.

This function is intended for target matrices where NaN means a task was not measured for that sample. Fitting receives the sparse target matrix unchanged. Metrics are calculated only over finite target entries, while the prediction table retains all sample-task predictions with an observed flag for filtering parity plots and diagnostics.

Source code in matgpr/validation.py 
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def evaluate_sparse_multitask_train_test_split(
    estimator,
    X,
    y,
    *,
    train_indices: Sequence[int] | None = None,
    test_indices: Sequence[int] | None = None,
    test_size: float | int = 0.2,
    train_size: float | int | None = None,
    random_state: int | None = None,
    shuffle: bool = True,
    model_name: str | None = None,
    task_names: Sequence[str] | None = None,
    return_std: bool = True,
    confidence_level: float = 0.95,
    include_observation_noise: bool | None = None,
    fit_params: Mapping[str, object] | None = None,
) -> SparseMultitaskTrainTestValidationResult:
    """Fit a sparse multitask estimator and evaluate observed target entries.

    This function is intended for target matrices where ``NaN`` means a task
    was not measured for that sample. Fitting receives the sparse target
    matrix unchanged. Metrics are calculated only over finite target entries,
    while the prediction table retains all sample-task predictions with an
    ``observed`` flag for filtering parity plots and diagnostics.
    """
    n_samples, _ = _validate_sparse_multitask_xy_length(X, y)
    labels = _sample_labels(y, n_samples)

    if train_indices is None and test_indices is None:
        train_indices, test_indices = train_test_split(
            np.arange(n_samples),
            train_size=train_size,
            test_size=test_size,
            random_state=random_state,
            shuffle=shuffle,
        )
    elif train_indices is None or test_indices is None:
        raise ValueError("train_indices and test_indices must be supplied together")
    else:
        train_indices = _to_index_array(train_indices, "train_indices", n_samples)
        test_indices = _to_index_array(test_indices, "test_indices", n_samples)

    train_indices = np.asarray(train_indices, dtype=int)
    test_indices = np.asarray(test_indices, dtype=int)
    _validate_split_indices(train_indices, test_indices, n_samples)

    fitted_estimator = _clone_estimator(estimator, random_state=random_state)
    X_train = _safe_index(X, train_indices)
    X_test = _safe_index(X, test_indices)
    y_train = _safe_index(y, train_indices)
    y_test = _safe_index(y, test_indices)
    model_name = model_name or _estimator_name(estimator)

    fitted_estimator.fit(X_train, y_train, **dict(fit_params or {}))
    y_train_pred, y_train_std, train_prediction_task_names = _predict_multitask_estimator(
        fitted_estimator,
        X_train,
        return_std=return_std,
        confidence_level=confidence_level,
        include_observation_noise=include_observation_noise,
    )
    y_test_pred, y_test_std, test_prediction_task_names = _predict_multitask_estimator(
        fitted_estimator,
        X_test,
        return_std=return_std,
        confidence_level=confidence_level,
        include_observation_noise=include_observation_noise,
    )
    fitted_task_names = getattr(fitted_estimator, "task_names_", None)
    resolved_task_names = _resolve_multitask_names(
        task_names=task_names,
        n_tasks=_to_2d_float_allow_nan(y_train, "y_train").shape[1],
        y=y,
        prediction_task_names=_first_available_task_names(
            fitted_task_names,
            train_prediction_task_names,
            test_prediction_task_names,
        ),
    )

    train_metrics = summarize_sparse_multitask_predictions(
        y_train,
        y_train_pred,
        y_train_std,
        task_names=resolved_task_names,
        model_name=model_name,
        split="train",
        confidence_level=confidence_level,
    )
    test_metrics = summarize_sparse_multitask_predictions(
        y_test,
        y_test_pred,
        y_test_std,
        task_names=resolved_task_names,
        model_name=model_name,
        split="test",
        confidence_level=confidence_level,
    )
    predictions = pd.concat(
        [
            _sparse_multitask_prediction_frame(
                model_name,
                "train",
                train_indices,
                labels,
                y_train,
                y_train_pred,
                y_train_std,
                task_names=resolved_task_names,
                confidence_level=confidence_level,
            ),
            _sparse_multitask_prediction_frame(
                model_name,
                "test",
                test_indices,
                labels,
                y_test,
                y_test_pred,
                y_test_std,
                task_names=resolved_task_names,
                confidence_level=confidence_level,
            ),
        ],
        ignore_index=True,
    )
    return SparseMultitaskTrainTestValidationResult(
        model_name=model_name,
        fitted_estimator=fitted_estimator,
        task_metrics=pd.concat([train_metrics, test_metrics], ignore_index=True),
        predictions=predictions,
        train_indices=train_indices,
        test_indices=test_indices,
    )

cross_validate_regressor(estimator, X, y, *, cv=5, shuffle=True, random_state=None, model_name=None, return_std=True, confidence_level=0.95, include_observation_noise=None, fit_params=None, store_train_predictions=False)

Run cross-validation and return fold metrics plus prediction rows.

Parameters:

Name Type Description Default
estimator

Any scikit-learn-style regressor with fit and predict.

 required
X

Feature matrix and target vector.

 required
y

Feature matrix and target vector.

 required
cv int | object

Number of folds or any splitter object with split(X, y).

 5
store_train_predictions bool

If True, include train predictions for each fold. Test predictions are always stored as out-of-fold predictions.

 False
Source code in matgpr/validation.py 
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def cross_validate_regressor(
    estimator,
    X,
    y,
    *,
    cv: int | object = 5,
    shuffle: bool = True,
    random_state: int | None = None,
    model_name: str | None = None,
    return_std: bool = True,
    confidence_level: float = 0.95,
    include_observation_noise: bool | None = None,
    fit_params: Mapping[str, object] | None = None,
    store_train_predictions: bool = False,
) -> CrossValidationResult:
    """Run cross-validation and return fold metrics plus prediction rows.

    Parameters
    ----------
    estimator
        Any scikit-learn-style regressor with ``fit`` and ``predict``.
    X, y
        Feature matrix and target vector.
    cv
        Number of folds or any splitter object with ``split(X, y)``.
    store_train_predictions
        If ``True``, include train predictions for each fold. Test predictions
        are always stored as out-of-fold predictions.
    """
    n_samples = _validate_xy_length(X, y)
    labels = _sample_labels(y, n_samples)
    resolved_model_name = model_name or _estimator_name(estimator)
    metric_rows = []
    prediction_tables = []

    for fold, (train_indices, test_indices) in enumerate(
        _iter_cv_splits(cv, X, y, shuffle=shuffle, random_state=random_state),
        start=1,
    ):
        seed = _derive_seed(random_state, fold)
        result = _fit_evaluate_indices(
            estimator,
            X,
            y,
            train_indices=np.asarray(train_indices, dtype=int),
            test_indices=np.asarray(test_indices, dtype=int),
            labels=labels,
            model_name=resolved_model_name,
            return_std=return_std,
            confidence_level=confidence_level,
            include_observation_noise=include_observation_noise,
            fit_params=fit_params,
            random_state=seed,
            context={"fold": fold},
        )
        metric_rows.append(
            {
                "model": resolved_model_name,
                "fold": fold,
                "n_train": len(train_indices),
                "n_test": len(test_indices),
                **result["metrics"],
            }
        )
        predictions = result["predictions"]
        if not store_train_predictions:
            predictions = predictions[predictions["split"] == "test"]
        prediction_tables.append(predictions)

    return CrossValidationResult(
        model_name=resolved_model_name,
        fold_metrics=pd.DataFrame(metric_rows),
        predictions=_concat_prediction_tables(prediction_tables),
    )

learning_curve(estimators, X, y, *, train_sizes=None, train_size_start=10, train_size_stop=100, train_size_step=10, train_size_unit='percent', n_splits=20, test_size=0.2, random_state=None, model_names=None, metrics=('RMSE', 'R2', 'MAE', 'r'), metric_splits=('test',), return_std=True, confidence_level=0.95, include_observation_noise=None, fit_params=None, store_predictions=False, min_train_samples=2)

Evaluate learning curves from repeated randomized holdout splits.

Parameters:

Name Type Description Default
estimators

One estimator, a sequence of estimators, a sequence of (name, estimator) pairs, or a mapping of model names to estimators.

 required
train_sizes Sequence[float | int] | None

Optional explicit train sizes. Values are interpreted according to train_size_unit. If omitted, values are generated from train_size_start to train_size_stop using train_size_step.

 None
train_size_unit str

"percent", "fraction", or "count".

 'percent'
n_splits int

Number of randomized splits per train-size point.

 20
metrics Sequence[str] | str

Metric names to summarize by default, for example ("RMSE", "R2").

 ('RMSE', 'R2', 'MAE', 'r')
metric_splits Sequence[str] | str

"test" for held-out metrics only or ("train", "test") for both train and test results.

 ('test',)
Notes

The returned runs dataframe includes train_size as the realized fraction of that split's training pool, train_size_percent as percent, and n_train as the sample count.

Source code in matgpr/validation.py 
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def learning_curve(
    estimators,
    X,
    y,
    *,
    train_sizes: Sequence[float | int] | None = None,
    train_size_start: float | int = 10,
    train_size_stop: float | int = 100,
    train_size_step: float | int = 10,
    train_size_unit: str = "percent",
    n_splits: int = 20,
    test_size: float | int = 0.2,
    random_state: int | None = None,
    model_names: str | Sequence[str] | None = None,
    metrics: Sequence[str] | str = ("RMSE", "R2", "MAE", "r"),
    metric_splits: Sequence[str] | str = ("test",),
    return_std: bool = True,
    confidence_level: float = 0.95,
    include_observation_noise: bool | None = None,
    fit_params: Mapping[str, object] | None = None,
    store_predictions: bool = False,
    min_train_samples: int = 2,
) -> LearningCurveResult:
    """Evaluate learning curves from repeated randomized holdout splits.

    Parameters
    ----------
    estimators
        One estimator, a sequence of estimators, a sequence of
        ``(name, estimator)`` pairs, or a mapping of model names to estimators.
    train_sizes
        Optional explicit train sizes. Values are interpreted according to
        ``train_size_unit``. If omitted, values are generated from
        ``train_size_start`` to ``train_size_stop`` using ``train_size_step``.
    train_size_unit
        ``"percent"``, ``"fraction"``, or ``"count"``.
    n_splits
        Number of randomized splits per train-size point.
    metrics
        Metric names to summarize by default, for example ``("RMSE", "R2")``.
    metric_splits
        ``"test"`` for held-out metrics only or ``("train", "test")`` for
        both train and test results.

    Notes
    -----
    The returned ``runs`` dataframe includes ``train_size`` as the realized
    fraction of that split's training pool, ``train_size_percent`` as percent,
    and ``n_train`` as the sample count.
    """
    n_samples = _validate_xy_length(X, y)
    if n_splits <= 0:
        raise ValueError("n_splits must be positive")
    if min_train_samples <= 0:
        raise ValueError("min_train_samples must be positive")

    model_specs = _normalize_estimators(estimators, model_names=model_names)
    normalized_train_sizes = _resolve_learning_curve_train_sizes(
        train_sizes,
        start=train_size_start,
        stop=train_size_stop,
        step=train_size_step,
        unit=train_size_unit,
    )
    metric_names = _normalize_metric_names(metrics)
    split_names = _normalize_metric_splits(metric_splits)
    labels = _sample_labels(y, n_samples)
    splitter = ShuffleSplit(
        n_splits=int(n_splits),
        test_size=test_size,
        random_state=random_state,
    )
    metric_rows = []
    prediction_tables = []

    for repeat, (train_pool_indices, test_indices) in enumerate(
        splitter.split(np.arange(n_samples)), start=1
    ):
        train_pool_indices = np.asarray(train_pool_indices, dtype=int)
        test_indices = np.asarray(test_indices, dtype=int)
        rng = np.random.default_rng(_derive_seed(random_state, repeat))

        for size_position, train_size_spec in enumerate(normalized_train_sizes, start=1):
            train_indices = _subsample_train_indices(
                train_pool_indices,
                train_size_spec["model_train_size"],
                rng=rng,
                min_train_samples=min_train_samples,
            )
            train_fraction = len(train_indices) / len(train_pool_indices)
            for model_position, (model_name, estimator) in enumerate(model_specs, start=1):
                seed = _derive_seed(random_state, repeat, size_position, model_position)
                result = _fit_evaluate_indices(
                    estimator,
                    X,
                    y,
                    train_indices=train_indices,
                    test_indices=test_indices,
                    labels=labels,
                    model_name=model_name,
                    return_std=return_std,
                    confidence_level=confidence_level,
                    include_observation_noise=include_observation_noise,
                    fit_params=fit_params,
                    random_state=seed,
                    context={
                        "repeat": repeat,
                        "train_size": train_fraction,
                        "train_size_percent": 100.0 * train_fraction,
                        "requested_train_size": train_size_spec["requested_train_size"],
                        "requested_train_size_unit": train_size_spec["requested_train_size_unit"],
                    },
                )
                metric_rows.append(
                    {
                        "model": model_name,
                        "repeat": repeat,
                        "train_size": train_fraction,
                        "train_size_percent": 100.0 * train_fraction,
                        "requested_train_size": train_size_spec["requested_train_size"],
                        "requested_train_size_unit": train_size_spec["requested_train_size_unit"],
                        "n_train": len(train_indices),
                        "n_test": len(test_indices),
                        **result["metrics"],
                    }
                )
                if store_predictions:
                    prediction_tables.append(result["predictions"])

    predictions = _concat_prediction_tables(prediction_tables) if store_predictions else None
    return LearningCurveResult(
        model_name=", ".join(name for name, _ in model_specs),
        runs=pd.DataFrame(metric_rows),
        predictions=predictions,
        metric_names=metric_names,
        metric_splits=split_names,
    )

multifidelity_learning_curve(estimators, X_high, y_high, *, low_fidelity_high=None, X_low=None, y_low=None, train_sizes=None, train_size_start=10, train_size_stop=100, train_size_step=10, train_size_unit='percent', n_splits=20, test_size=0.2, random_state=None, model_names=None, metrics=('RMSE', 'R2', 'MAE', 'r'), metric_splits=('test',), return_std=True, confidence_level=0.95, include_observation_noise=None, include_low_fidelity_uncertainty=None, fit_params=None, store_predictions=False, min_train_samples=2)

Evaluate high-fidelity learning curves for multi-fidelity estimators.

X_high and y_high define the scarce high-fidelity dataset whose train size is varied. Use low_fidelity_high when low-fidelity values are available at the same high-fidelity rows. Alternatively, provide a fixed low-fidelity training set through X_low and y_low so each fitted estimator can build or reuse a low-fidelity surrogate.

The returned runs dataframe contains high-fidelity train/test metrics. When store_predictions=True, the prediction table also includes low-fidelity and correction components when the estimator exposes them.

Source code in matgpr/validation.py 
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def multifidelity_learning_curve(
    estimators,
    X_high,
    y_high,
    *,
    low_fidelity_high=None,
    X_low=None,
    y_low=None,
    train_sizes: Sequence[float | int] | None = None,
    train_size_start: float | int = 10,
    train_size_stop: float | int = 100,
    train_size_step: float | int = 10,
    train_size_unit: str = "percent",
    n_splits: int = 20,
    test_size: float | int = 0.2,
    random_state: int | None = None,
    model_names: str | Sequence[str] | None = None,
    metrics: Sequence[str] | str = ("RMSE", "R2", "MAE", "r"),
    metric_splits: Sequence[str] | str = ("test",),
    return_std: bool = True,
    confidence_level: float = 0.95,
    include_observation_noise: bool | None = None,
    include_low_fidelity_uncertainty: bool | None = None,
    fit_params: Mapping[str, object] | None = None,
    store_predictions: bool = False,
    min_train_samples: int = 2,
) -> LearningCurveResult:
    """Evaluate high-fidelity learning curves for multi-fidelity estimators.

    ``X_high`` and ``y_high`` define the scarce high-fidelity dataset whose
    train size is varied. Use ``low_fidelity_high`` when low-fidelity values
    are available at the same high-fidelity rows. Alternatively, provide a
    fixed low-fidelity training set through ``X_low`` and ``y_low`` so each
    fitted estimator can build or reuse a low-fidelity surrogate.

    The returned ``runs`` dataframe contains high-fidelity train/test metrics.
    When ``store_predictions=True``, the prediction table also includes
    low-fidelity and correction components when the estimator exposes them.
    """
    n_samples = _validate_xy_length(X_high, y_high)
    if n_splits <= 0:
        raise ValueError("n_splits must be positive")
    if min_train_samples <= 0:
        raise ValueError("min_train_samples must be positive")
    _validate_multifidelity_low_inputs(
        X_high,
        low_fidelity_high=low_fidelity_high,
        X_low=X_low,
        y_low=y_low,
    )

    model_specs = _normalize_estimators(estimators, model_names=model_names)
    normalized_train_sizes = _resolve_learning_curve_train_sizes(
        train_sizes,
        start=train_size_start,
        stop=train_size_stop,
        step=train_size_step,
        unit=train_size_unit,
    )
    metric_names = _normalize_metric_names(metrics)
    split_names = _normalize_metric_splits(metric_splits)
    labels = _sample_labels(y_high, n_samples)
    splitter = ShuffleSplit(
        n_splits=int(n_splits),
        test_size=test_size,
        random_state=random_state,
    )
    metric_rows = []
    prediction_tables = []

    for repeat, (train_pool_indices, test_indices) in enumerate(
        splitter.split(np.arange(n_samples)), start=1
    ):
        train_pool_indices = np.asarray(train_pool_indices, dtype=int)
        test_indices = np.asarray(test_indices, dtype=int)
        rng = np.random.default_rng(_derive_seed(random_state, repeat))

        for size_position, train_size_spec in enumerate(normalized_train_sizes, start=1):
            train_indices = _subsample_train_indices(
                train_pool_indices,
                train_size_spec["model_train_size"],
                rng=rng,
                min_train_samples=min_train_samples,
            )
            train_fraction = len(train_indices) / len(train_pool_indices)
            for model_position, (model_name, estimator) in enumerate(model_specs, start=1):
                seed = _derive_seed(random_state, repeat, size_position, model_position)
                result = _fit_evaluate_multifidelity_indices(
                    estimator,
                    X_high,
                    y_high,
                    low_fidelity_high=low_fidelity_high,
                    X_low=X_low,
                    y_low=y_low,
                    train_indices=train_indices,
                    test_indices=test_indices,
                    labels=labels,
                    model_name=model_name,
                    return_std=return_std,
                    confidence_level=confidence_level,
                    include_observation_noise=include_observation_noise,
                    include_low_fidelity_uncertainty=include_low_fidelity_uncertainty,
                    fit_params=fit_params,
                    random_state=seed,
                    context={
                        "repeat": repeat,
                        "train_size": train_fraction,
                        "train_size_percent": 100.0 * train_fraction,
                        "requested_train_size": train_size_spec["requested_train_size"],
                        "requested_train_size_unit": train_size_spec["requested_train_size_unit"],
                    },
                )
                metric_rows.append(
                    {
                        "model": model_name,
                        "repeat": repeat,
                        "train_size": train_fraction,
                        "train_size_percent": 100.0 * train_fraction,
                        "requested_train_size": train_size_spec["requested_train_size"],
                        "requested_train_size_unit": train_size_spec["requested_train_size_unit"],
                        "n_train": len(train_indices),
                        "n_test": len(test_indices),
                        "rho": result["rho"],
                        "intercept": result["intercept"],
                        **result["metrics"],
                    }
                )
                if store_predictions:
                    prediction_tables.append(result["predictions"])

    predictions = _concat_prediction_tables(prediction_tables) if store_predictions else None
    return LearningCurveResult(
        model_name=", ".join(name for name, _ in model_specs),
        runs=pd.DataFrame(metric_rows),
        predictions=predictions,
        metric_names=metric_names,
        metric_splits=split_names,
    )

cokriging_learning_curve(estimators, X, y, fidelity, *, target_fidelity=None, low_fidelity=None, fidelity_order=None, sample_id=None, train_sizes=None, train_size_start=10, train_size_stop=100, train_size_step=10, train_size_unit='percent', n_splits=20, test_size=0.2, random_state=None, model_names=None, metrics=('RMSE', 'R2', 'MAE', 'r'), metric_splits=('test',), return_std=True, confidence_level=0.95, include_observation_noise=None, fit_params=None, store_predictions=False, min_train_samples=2)

Evaluate target-fidelity learning curves for row-wise co-kriging data.

X, y, and fidelity describe one observation table containing both lower- and target-fidelity rows. Each split is drawn only from the target-fidelity rows. All lower-fidelity observations remain available for fitting, so n_train in the returned run table is the number of target-fidelity training rows, while n_fit also includes the fixed lower-fidelity rows.

Source code in matgpr/validation.py 
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def cokriging_learning_curve(
    estimators,
    X,
    y,
    fidelity,
    *,
    target_fidelity: str | None = None,
    low_fidelity: str | None = None,
    fidelity_order: Sequence[str] | None = None,
    sample_id=None,
    train_sizes: Sequence[float | int] | None = None,
    train_size_start: float | int = 10,
    train_size_stop: float | int = 100,
    train_size_step: float | int = 10,
    train_size_unit: str = "percent",
    n_splits: int = 20,
    test_size: float | int = 0.2,
    random_state: int | None = None,
    model_names: str | Sequence[str] | None = None,
    metrics: Sequence[str] | str = ("RMSE", "R2", "MAE", "r"),
    metric_splits: Sequence[str] | str = ("test",),
    return_std: bool = True,
    confidence_level: float = 0.95,
    include_observation_noise: bool | None = None,
    fit_params: Mapping[str, object] | None = None,
    store_predictions: bool = False,
    min_train_samples: int = 2,
) -> LearningCurveResult:
    """Evaluate target-fidelity learning curves for row-wise co-kriging data.

    ``X``, ``y``, and ``fidelity`` describe one observation table containing
    both lower- and target-fidelity rows. Each split is drawn only from the
    target-fidelity rows. All lower-fidelity observations remain available for
    fitting, so ``n_train`` in the returned run table is the number of
    target-fidelity training rows, while ``n_fit`` also includes the fixed
    lower-fidelity rows.
    """
    n_samples = _validate_xy_length(X, y)
    if n_splits <= 0:
        raise ValueError("n_splits must be positive")
    if min_train_samples <= 0:
        raise ValueError("min_train_samples must be positive")

    model_specs = _normalize_estimators(estimators, model_names=model_names)
    normalized_train_sizes = _resolve_learning_curve_train_sizes(
        train_sizes,
        start=train_size_start,
        stop=train_size_stop,
        step=train_size_step,
        unit=train_size_unit,
    )
    metric_names = _normalize_metric_names(metrics)
    split_names = _normalize_metric_splits(metric_splits)
    labels = _sample_labels(y, n_samples)
    fidelity_labels = _to_fidelity_label_array(fidelity, n_samples=n_samples)
    sample_id_array = _resolve_optional_row_values(sample_id, n_samples=n_samples, name="sample_id")
    fidelity_names, target_name, low_name = _resolve_cokriging_validation_levels(
        fidelity_labels,
        estimator=model_specs[0][1],
        target_fidelity=target_fidelity,
        low_fidelity=low_fidelity,
        fidelity_order=fidelity_order,
    )
    target_positions = np.flatnonzero(fidelity_labels == target_name)
    if target_positions.size < 2:
        raise ValueError("At least two target-fidelity rows are required for validation")

    splitter = ShuffleSplit(
        n_splits=int(n_splits),
        test_size=test_size,
        random_state=random_state,
    )
    metric_rows = []
    prediction_tables = []

    for repeat, (train_pool_relative, test_relative) in enumerate(
        splitter.split(target_positions),
        start=1,
    ):
        train_pool_indices = target_positions[np.asarray(train_pool_relative, dtype=int)]
        test_indices = target_positions[np.asarray(test_relative, dtype=int)]
        rng = np.random.default_rng(_derive_seed(random_state, repeat))

        for size_position, train_size_spec in enumerate(normalized_train_sizes, start=1):
            train_indices = _subsample_train_indices(
                train_pool_indices,
                train_size_spec["model_train_size"],
                rng=rng,
                min_train_samples=min_train_samples,
            )
            train_fraction = len(train_indices) / len(train_pool_indices)
            fit_indices, lower_fidelity_indices = _cokriging_fit_indices(
                fidelity_labels,
                target_fidelity=target_name,
                train_indices=train_indices,
            )
            for model_position, (model_name, estimator) in enumerate(model_specs, start=1):
                seed = _derive_seed(random_state, repeat, size_position, model_position)
                result = _fit_evaluate_cokriging_indices(
                    estimator,
                    X,
                    y,
                    fidelity_labels=fidelity_labels,
                    sample_id=sample_id_array,
                    fit_indices=fit_indices,
                    train_indices=train_indices,
                    test_indices=test_indices,
                    labels=labels,
                    fidelity_names=fidelity_names,
                    target_fidelity=target_name,
                    low_fidelity=low_name,
                    model_name=model_name,
                    return_std=return_std,
                    confidence_level=confidence_level,
                    include_observation_noise=include_observation_noise,
                    fit_params=fit_params,
                    random_state=seed,
                    context={
                        "repeat": repeat,
                        "train_size": train_fraction,
                        "train_size_percent": 100.0 * train_fraction,
                        "requested_train_size": train_size_spec["requested_train_size"],
                        "requested_train_size_unit": train_size_spec["requested_train_size_unit"],
                        "target_fidelity": target_name,
                        "low_fidelity": low_name,
                        "n_lower_fidelity": len(lower_fidelity_indices),
                    },
                )
                metric_rows.append(
                    {
                        "model": model_name,
                        "repeat": repeat,
                        "train_size": train_fraction,
                        "train_size_percent": 100.0 * train_fraction,
                        "requested_train_size": train_size_spec["requested_train_size"],
                        "requested_train_size_unit": train_size_spec["requested_train_size_unit"],
                        "n_train": len(train_indices),
                        "n_test": len(test_indices),
                        "n_fit": len(fit_indices),
                        "n_lower_fidelity": len(lower_fidelity_indices),
                        "target_fidelity": target_name,
                        "low_fidelity": low_name,
                        "rho": result["rho"],
                        **result["metrics"],
                    }
                )
                if store_predictions:
                    prediction_tables.append(result["predictions"])

    predictions = _concat_prediction_tables(prediction_tables) if store_predictions else None
    return LearningCurveResult(
        model_name=", ".join(name for name, _ in model_specs),
        runs=pd.DataFrame(metric_rows),
        predictions=predictions,
        metric_names=metric_names,
        metric_splits=split_names,
    )