.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/miscellaneous/plot_kernel_ridge_regression.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_miscellaneous_plot_kernel_ridge_regression.py: ============================================= Comparison of kernel ridge regression and SVR ============================================= Both kernel ridge regression (KRR) and SVR learn a non-linear function by employing the kernel trick, i.e., they learn a linear function in the space induced by the respective kernel which corresponds to a non-linear function in the original space. They differ in the loss functions (ridge versus epsilon-insensitive loss). In contrast to SVR, fitting a KRR can be done in closed-form and is typically faster for medium-sized datasets. On the other hand, the learned model is non-sparse and thus slower than SVR at prediction-time. This example illustrates both methods on an artificial dataset, which consists of a sinusoidal target function and strong noise added to every fifth datapoint. .. GENERATED FROM PYTHON SOURCE LINES 22-24 Authors: The scikit-learn developers SPDX-License-Identifier: BSD-3-Clause .. GENERATED FROM PYTHON SOURCE LINES 26-28 Generate sample data -------------------- .. GENERATED FROM PYTHON SOURCE LINES 28-40 .. code-block:: Python import numpy as np rng = np.random.RandomState(42) X = 5 * rng.rand(10000, 1) y = np.sin(X).ravel() # Add noise to targets y[::5] += 3 * (0.5 - rng.rand(X.shape[0] // 5)) X_plot = np.linspace(0, 5, 100000)[:, None] .. GENERATED FROM PYTHON SOURCE LINES 41-43 Construct the kernel-based regression models -------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 43-60 .. code-block:: Python from sklearn.kernel_ridge import KernelRidge from sklearn.model_selection import GridSearchCV from sklearn.svm import SVR train_size = 100 svr = GridSearchCV( SVR(kernel="rbf", gamma=0.1), param_grid={"C": [1e0, 1e1, 1e2, 1e3], "gamma": np.logspace(-2, 2, 5)}, ) kr = GridSearchCV( KernelRidge(kernel="rbf", gamma=0.1), param_grid={"alpha": [1e0, 0.1, 1e-2, 1e-3], "gamma": np.logspace(-2, 2, 5)}, ) .. GENERATED FROM PYTHON SOURCE LINES 61-63 Compare times of SVR and Kernel Ridge Regression ------------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 63-91 .. code-block:: Python import time t0 = time.time() svr.fit(X[:train_size], y[:train_size]) svr_fit = time.time() - t0 print(f"Best SVR with params: {svr.best_params_} and R2 score: {svr.best_score_:.3f}") print("SVR complexity and bandwidth selected and model fitted in %.3f s" % svr_fit) t0 = time.time() kr.fit(X[:train_size], y[:train_size]) kr_fit = time.time() - t0 print(f"Best KRR with params: {kr.best_params_} and R2 score: {kr.best_score_:.3f}") print("KRR complexity and bandwidth selected and model fitted in %.3f s" % kr_fit) sv_ratio = svr.best_estimator_.support_.shape[0] / train_size print("Support vector ratio: %.3f" % sv_ratio) t0 = time.time() y_svr = svr.predict(X_plot) svr_predict = time.time() - t0 print("SVR prediction for %d inputs in %.3f s" % (X_plot.shape[0], svr_predict)) t0 = time.time() y_kr = kr.predict(X_plot) kr_predict = time.time() - t0 print("KRR prediction for %d inputs in %.3f s" % (X_plot.shape[0], kr_predict)) .. rst-class:: sphx-glr-script-out .. code-block:: none Best SVR with params: {'C': 1.0, 'gamma': np.float64(0.1)} and R2 score: 0.737 SVR complexity and bandwidth selected and model fitted in 0.387 s Best KRR with params: {'alpha': 0.1, 'gamma': np.float64(0.1)} and R2 score: 0.723 KRR complexity and bandwidth selected and model fitted in 0.170 s Support vector ratio: 0.340 SVR prediction for 100000 inputs in 0.088 s KRR prediction for 100000 inputs in 0.097 s .. GENERATED FROM PYTHON SOURCE LINES 92-94 Look at the results ------------------- .. GENERATED FROM PYTHON SOURCE LINES 94-122 .. code-block:: Python import matplotlib.pyplot as plt sv_ind = svr.best_estimator_.support_ plt.scatter( X[sv_ind], y[sv_ind], c="r", s=50, label="SVR support vectors", zorder=2, edgecolors=(0, 0, 0), ) plt.scatter(X[:100], y[:100], c="k", label="data", zorder=1, edgecolors=(0, 0, 0)) plt.plot( X_plot, y_svr, c="r", label="SVR (fit: %.3fs, predict: %.3fs)" % (svr_fit, svr_predict), ) plt.plot( X_plot, y_kr, c="g", label="KRR (fit: %.3fs, predict: %.3fs)" % (kr_fit, kr_predict) ) plt.xlabel("data") plt.ylabel("target") plt.title("SVR versus Kernel Ridge") _ = plt.legend() .. image-sg:: /auto_examples/miscellaneous/images/sphx_glr_plot_kernel_ridge_regression_001.png :alt: SVR versus Kernel Ridge :srcset: /auto_examples/miscellaneous/images/sphx_glr_plot_kernel_ridge_regression_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 123-135 The previous figure compares the learned model of KRR and SVR when both complexity/regularization and bandwidth of the RBF kernel are optimized using grid-search. The learned functions are very similar; however, fitting KRR is approximately 3-4 times faster than fitting SVR (both with grid-search). Prediction of 100000 target values could be in theory approximately three times faster with SVR since it has learned a sparse model using only approximately 1/3 of the training datapoints as support vectors. However, in practice, this is not necessarily the case because of implementation details in the way the kernel function is computed for each model that can make the KRR model as fast or even faster despite computing more arithmetic operations. .. GENERATED FROM PYTHON SOURCE LINES 137-139 Visualize training and prediction times --------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 139-180 .. code-block:: Python plt.figure() sizes = np.logspace(1, 3.8, 7).astype(int) for name, estimator in { "KRR": KernelRidge(kernel="rbf", alpha=0.01, gamma=10), "SVR": SVR(kernel="rbf", C=1e2, gamma=10), }.items(): train_time = [] test_time = [] for train_test_size in sizes: t0 = time.time() estimator.fit(X[:train_test_size], y[:train_test_size]) train_time.append(time.time() - t0) t0 = time.time() estimator.predict(X_plot[:1000]) test_time.append(time.time() - t0) plt.plot( sizes, train_time, "o-", color="r" if name == "SVR" else "g", label="%s (train)" % name, ) plt.plot( sizes, test_time, "o--", color="r" if name == "SVR" else "g", label="%s (test)" % name, ) plt.xscale("log") plt.yscale("log") plt.xlabel("Train size") plt.ylabel("Time (seconds)") plt.title("Execution Time") _ = plt.legend(loc="best") .. image-sg:: /auto_examples/miscellaneous/images/sphx_glr_plot_kernel_ridge_regression_002.png :alt: Execution Time :srcset: /auto_examples/miscellaneous/images/sphx_glr_plot_kernel_ridge_regression_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 181-189 This figure compares the time for fitting and prediction of KRR and SVR for different sizes of the training set. Fitting KRR is faster than SVR for medium-sized training sets (less than a few thousand samples); however, for larger training sets SVR scales better. With regard to prediction time, SVR should be faster than KRR for all sizes of the training set because of the learned sparse solution, however this is not necessarily the case in practice because of implementation details. Note that the degree of sparsity and thus the prediction time depends on the parameters epsilon and C of the SVR. .. GENERATED FROM PYTHON SOURCE LINES 191-193 Visualize the learning curves ----------------------------- .. GENERATED FROM PYTHON SOURCE LINES 193-218 .. code-block:: Python from sklearn.model_selection import LearningCurveDisplay _, ax = plt.subplots() svr = SVR(kernel="rbf", C=1e1, gamma=0.1) kr = KernelRidge(kernel="rbf", alpha=0.1, gamma=0.1) common_params = { "X": X[:100], "y": y[:100], "train_sizes": np.linspace(0.1, 1, 10), "scoring": "neg_mean_squared_error", "negate_score": True, "score_name": "Mean Squared Error", "score_type": "test", "std_display_style": None, "ax": ax, } LearningCurveDisplay.from_estimator(svr, **common_params) LearningCurveDisplay.from_estimator(kr, **common_params) ax.set_title("Learning curves") ax.legend(handles=ax.get_legend_handles_labels()[0], labels=["SVR", "KRR"]) plt.show() .. image-sg:: /auto_examples/miscellaneous/images/sphx_glr_plot_kernel_ridge_regression_003.png :alt: Learning curves :srcset: /auto_examples/miscellaneous/images/sphx_glr_plot_kernel_ridge_regression_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 5.862 seconds) .. _sphx_glr_download_auto_examples_miscellaneous_plot_kernel_ridge_regression.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/miscellaneous/plot_kernel_ridge_regression.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_kernel_ridge_regression.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_kernel_ridge_regression.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_kernel_ridge_regression.zip ` .. include:: plot_kernel_ridge_regression.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_