1D smoothing with Polyfit1DModel

Polyfit1DModel performs local polynomial regression with a selectable kernel. Bandwidth can be chosen automatically via GCV or CV. After fitting, predictions are computed efficiently through internal interpolation on a regular grid.

Basic usage

import numpy as np
from pflm.smooth import Polyfit1DModel, KernelType

rng = np.random.default_rng(0)
X = np.linspace(0, 1, 200)
y_true = np.sin(2 * np.pi * X)
y = y_true + rng.normal(0, 0.1, size=X.shape)

model = Polyfit1DModel(
    kernel_type=KernelType.GAUSSIAN,
    degree=1,
    deriv=0,
    interp_kind="spline",
)
model.fit(X, y, bandwidth_selection_method="gcv", num_points_reg_grid=150)
print("Selected bandwidth:", model.bandwidth_)

Xq = np.linspace(0, 1, 100)
yq = model.predict(Xq)  # uses internal interpolation
print("Max error:", np.max(np.abs(yq - np.sin(2 * np.pi * Xq))))

Kernel and bandwidth options

The kernel_type parameter supports several kernels. You can also provide a fixed bandwidth or use CV with a custom candidate grid.

# Epanechnikov kernel with cross-validation
model_cv = Polyfit1DModel(
    kernel_type=KernelType.EPANECHNIKOV,
    degree=1,
    interp_kind="linear",
    random_seed=42,
)
model_cv.fit(
    X, y,
    bandwidth_selection_method="cv",
    cv_folds=5,
    num_bw_candidates=30,
)
print("CV bandwidth:", model_cv.bandwidth_)

# Or supply a known bandwidth
model_fixed = Polyfit1DModel(kernel_type=KernelType.GAUSSIAN)
model_fixed.fit(X, y, bandwidth=0.08)
print("Fixed bandwidth:", model_fixed.bandwidth_)

Weighted observations

weights = np.ones_like(X)
weights[:50] = 2.0  # up-weight the first 50 points
model.fit(X, y, sample_weight=weights, bandwidth_selection_method="gcv")