Note

This example is in part a copy of plot_kernel_ridge_regressions by Jan Hendrik Metzen found in the package Scikit-Learn.

Nadaraya-Watos (NW) regression learns a non-linear function by using a kernel- weighted average of the data. Fitting NW can be done in closed-form and is typically very fast. However, the learned model is non-sparse and thus suffers at prediction-time.

This example illustrates NW on an artificial dataset, which consists of a sinusoidal target function and strong noise added to every fifth datapoint.

Out:

GridSearchCV 5 fold cross validation fitted in 0.20 s
optimal bandwidth found: 3.16
NadarayaWatsonCV leave-one-out cross validation fitted in 0.02 s
optimal bandwidth found: 3.162


# Authors: Joseph Knox <josephk@alleninstitute.org>

# NOTE: modified from plot_kernel_ridge_regression.py by Jan Hendrik Metzen
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from __future__ import division, print_function
import time

import numpy as np
import matplotlib.pyplot as plt

from sklearn.model_selection import GridSearchCV

print(__doc__)

rng = np.random.RandomState(0)

# #############################################################################
# Generate sample data
X = 5 * rng.rand(10000, 1)
y = np.sin(X).ravel()

y[::5] += 3 * (0.5 - rng.rand(X.shape[0] // 5))

X_plot = np.linspace(0, 5, 1e3)[:, None]

# #############################################################################
# Fit regression model
train_size = 100
param_grid=dict(kernel=["rbf"], gamma=np.logspace(-2, 2, 25))

# fit 5-fold using GridSearch
t0 = time.time()
nw_gs.fit(X[:train_size], y[:train_size])
gs_fit = time.time() - t0
print("GridSearchCV 5 fold cross validation fitted in %.2f s" % gs_fit)
print("\toptimal bandwidth found: %.2f" % nw_gs.best_estimator_.gamma)

t0 = time.time()
nw_cv.fit(X[:train_size], y[:train_size])
cv_fit = time.time() - t0
print("NadarayaWatsonCV leave-one-out cross validation fitted in %.2f s" % cv_fit)
print("\toptimal bandwidth found: %.3f" % nw_cv.gamma)

# predict
y_gs = nw_gs.predict(X_plot)
y_cv = nw_cv.predict(X_plot)

# #############################################################################
# Look at the results
plt.scatter(X[:100], y[:100], c='k', label='data', zorder=1,
edgecolors=(0, 0, 0))
plt.plot(X_plot, y_gs, 'c-', lw=3, label='5-Fold GridSearchCV')
plt.plot(X_plot, y_cv, 'r:', lw=3, label='LOO NadarayaWatsonCV')
plt.xlabel('data')
plt.ylabel('target')