Smoothing Spline

This repository provides a minimal, high-performance implementation of a smoothing spline, similar to the smooth.spline function in R. The core logic is implemented in C++ for speed, with convenient Python bindings provided by pybind11. The package is designed to be familiar to users of scikit-learn.

Key Features

• High Performance: Core computations are in C++, leveraging the Eigen library for efficient linear algebra.
• Flexible Smoothing Control: Specify smoothness by either degrees of freedom (df) or a penalty term (lambda).
• Automatic GCV: Includes a method to find the optimal smoothing parameter via Generalized Cross-Validation (GCV).
• Extrapolation: Supports linear extrapolation for points outside the training data range.
• R Compatibility: Tested against R's smooth.spline for comparable results.
• Scikit-learn Style API (NOT): The SplineSmoother class uses smooth(y)/predict(x). It is not an sklearn estimator, but will be / is wrapped into one in ISLP. This is intentional, as there are use cases for this as a lower level object where weights may be updated and the smoother be refit to new data.

Installation

For standard usage, you can install the package directly from this repository using pip:

pip install .

For development, you can install the package in editable mode with the --no-build-isolation flag:

pip install -e . --no-build-isolation

Usage Example

Here is a simple example of how to fit a smoothing spline to noisy data.

import numpy as np
import matplotlib.pyplot as plt
from scatter_smooth.fitter import SplineSmoother

# 1. Generate some noisy data
rng = np.random.default_rng(0)
x = np.linspace(0, 1, 100)
y_true = np.sin(2 * np.pi * x)
y_noisy = y_true + rng.standard_normal(100) * 0.2

# 2. Fit the smoothing spline
# Specify the desired degrees of freedom (df)
fitter = SplineSmoother(x, df=8)
fitter.smooth(y_noisy)

# 3. Predict on a new set of points
x_pred = np.linspace(0, 1, 200)
y_pred = fitter.predict(x_pred)

# 4. Plot the results
plt.figure(figsize=(10, 6))
plt.scatter(x, y_noisy, label='Noisy Data', alpha=0.6)
plt.plot(x, y_true, 'g--', label='True Function')
plt.plot(x_pred, y_pred, 'r-', label='Fitted Spline (df=8)', linewidth=2)
plt.legend()
plt.title('Smoothing Spline Fit')
plt.xlabel('x')
plt.ylabel('y')
plt.show()

Building from Source

To build the package from source, you will need a C++ compiler compatible with C++11 and the required Python development headers. The build process is managed by setuptools and pybind11.

1. Clone the repository:

   git clone https://github.com/your-username/scatter_smooth.git
   cd scatter_smooth
   

2. Install the dependencies and build the extension:

   pip install -r requirements.txt # Or install numpy, pybind11 manually
   pip install .
   

Running Tests

The project uses pytest for testing. The tests compare the output against R's smooth.spline and verify internal consistency. To run the tests, you will need to install pytest and rpy2.

pip install pytest rpy2
pytest

Note: An installation of R is required for the rpy2 comparison tests to run.

License

This project is licensed under the BSD-3-Clause License. See the LICENSE file for details.