pflm.smooth.Polyfit2DModel#

class Polyfit2DModel(kernel_type: KernelType = KernelType.GAUSSIAN, degree: int = 1, deriv1: int = 0, deriv2: int = 0, interp_kind: Literal['linear', 'spline'] = 'linear', random_seed: int | None = None)[source][source]#

Bases: BaseEstimator, RegressorMixin

Local polynomial (2D) regression with kernel smoothing and interpolation.

Parameters:

kernel_typeKernelType, default=KernelType.GAUSSIAN: Kernel used for smoothing.
degreeint, default=1: Polynomial degree (>= 1).
deriv1int, default=0: Derivative order along the first dimension (>= 0).
deriv2int, default=0: Derivative order along the second dimension (>= 0).
interp_kind{“linear”, “spline”}, default=”linear”: Interpolation method used for fast prediction.
random_seedint, optional: Random seed for reproducibility (e.g., CV shuffles).

Attributes:

X_np.ndarray of shape (n_samples, 2): Training inputs.
y_np.ndarray of shape (n_samples,): Training targets.
sample_weight_np.ndarray of shape (n_samples,): Sample weights.
reg_grid1_np.ndarray of shape (m1,): Interpolation grid along the first dimension.
reg_grid2_np.ndarray of shape (m2,): Interpolation grid along the second dimension.
reg_fitted_values_np.ndarray of shape (m1, m2): Fitted values evaluated on the interpolation grid mesh.
obs_grid1_np.ndarray of shape (n_obs_grid1,): Unique observed grid from X[:, 0].
obs_grid2_np.ndarray of shape (n_obs_grid2,): Unique observed grid from X[:, 1].
bandwidth1_float: Selected/used bandwidth for the first dimension.
bandwidth2_float: Selected/used bandwidth for the second dimension.
bandwidth_selection_results_dict: Selection details including candidates, method, and chosen pair.

See also

Polyfit1DModel: Local polynomial regression in 1D.

Examples

>>> import numpy as np
>>> from pflm.smooth import Polyfit2DModel
>>> rng = np.random.default_rng(42)
>>> n = 200
>>> X = rng.uniform(0, 1, (n, 2))
>>> y = np.sin(X[:, 0] * np.pi) * np.cos(X[:, 1] * np.pi) + rng.normal(0, 0.1, n)
>>> model = Polyfit2DModel().fit(X, y)
>>> model.bandwidth1_ > 0 and model.bandwidth2_ > 0
True
>>> y_pred = model.predict(np.array([0.5, 0.8]), np.array([0.5, 0.8]))
>>> y_pred.shape
(2,)

fit(X: ndarray | list[list[float]], y: ndarray | list[float], sample_weight: ndarray | list[float] | None = None, bandwidth1: float | None = None, bandwidth2: float | None = None, reg_grid1: ndarray | list[float] | None = None, reg_grid2: ndarray | list[float] | None = None, num_bw_candidates: int = 21, bandwidth_selection_method: Literal['cv', 'gcv'] = 'gcv', num_points_reg_grid: int = 100, same_bandwidth_for_2dim: bool = False, custom_bw_candidates: ndarray | None = None, cv_folds: int = 5)[source][source]#

Fit the 2D local polynomial model with kernel smoothing.

Parameters:

Xarray-like of shape (n_samples, 2): Training inputs.
yarray-like of shape (n_samples,): Training targets.
sample_weightarray-like of shape (n_samples,), optional: Sample weights.
bandwidth1float, optional: Bandwidth for the first axis.
bandwidth2float, optional: Bandwidth for the second axis.
reg_grid1array-like of shape (m1,), optional: Interpolation grid on axis-1. If None, a uniform grid is created.
reg_grid2array-like of shape (m2,), optional: Interpolation grid on axis-2. If None, a uniform grid is created.
num_bw_candidatesint, default=21
bandwidth_selection_method{“cv”, “gcv”}, default=”gcv”
num_points_reg_gridint, default=100: Number of points for each axis of the internal interpolation grid (used if reg_grid1/reg_grid2 are None).
same_bandwidth_for_2dimbool, default=False
custom_bw_candidatesnp.ndarray, optional
cv_foldsint, default=5

Returns:

Polyfit2DModel: Fitted estimator (self).

Raises:

ValueError: If inputs are invalid or selection arguments are inconsistent.

fitted_values() → ndarray[source][source]#

Return fitted values on the model’s 2D interpolation grid.

Returns:

np.ndarray of shape (len(reg_grid1_) * len(reg_grid2_),): Fitted values evaluated on the 2D interpolation mesh.

get_fitted_grids() → tuple[ndarray, ndarray][source][source]#

Return interpolation grids and fitted values.

Returns:

reg_grid1np.ndarray of shape (m1,): Copy of reg_grid1_.
reg_grid2np.ndarray of shape (m2,): Copy of reg_grid2_.
reg_fitted_valuesnp.ndarray of shape (m1, m2): Copy of reg_fitted_values_.

predict(X1: ndarray, X2: ndarray, use_model_interp: bool = True) → ndarray[source][source]#

Predict responses on a 2D grid.

Parameters:

X1np.ndarray of shape (n_x1,): Query points along axis-1.
X2np.ndarray of shape (n_x2,): Query points along axis-2.
use_model_interpbool, default=True: If True, interpolate from the fitted grid; if False, evaluate directly.

Returns:

np.ndarray of shape (n_x2, n_x1): Predicted values (note the row-major order).

Raises:

sklearn.exceptions.NotFittedError: If the model is not fitted.

Configure whether metadata should be requested to be passed to the fit method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config()). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Parameters:

bandwidth1str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for bandwidth1 parameter in fit.
bandwidth2str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for bandwidth2 parameter in fit.
bandwidth_selection_methodstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for bandwidth_selection_method parameter in fit.
custom_bw_candidatesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for custom_bw_candidates parameter in fit.
cv_foldsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for cv_folds parameter in fit.
num_bw_candidatesstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for num_bw_candidates parameter in fit.
num_points_reg_gridstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for num_points_reg_grid parameter in fit.
reg_grid1str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for reg_grid1 parameter in fit.
reg_grid2str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for reg_grid2 parameter in fit.
same_bandwidth_for_2dimstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for same_bandwidth_for_2dim parameter in fit.
sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for sample_weight parameter in fit.

Returns:

selfobject: The updated object.

Configure whether metadata should be requested to be passed to the predict method.

The options for each parameter are:

True: metadata is requested, and passed to predict if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to predict.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Parameters:

X1str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for X1 parameter in predict.
X2str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for X2 parameter in predict.
use_model_interpstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for use_model_interp parameter in predict.

Returns:

selfobject: The updated object.

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → Polyfit2DModel#

Configure whether metadata should be requested to be passed to the score method.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for sample_weight parameter in score.

Returns:

selfobject: The updated object.