.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/mlearning/quality_measure/plot_mse.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_mlearning_quality_measure_plot_mse.py: MSE example - test-train split ============================== In this example we consider a polynomial linear regression, splitting the data into two sets. We measure the quality of the regression by comparing the predictions with the output on the test set. .. GENERATED FROM PYTHON SOURCE LINES 32-49 .. code-block:: default from __future__ import absolute_import, division, print_function, unicode_literals from builtins import int import matplotlib.pyplot as plt from future import standard_library from numpy import arange, argmin, hstack, linspace, sort from numpy.random import choice, normal, seed from gemseo.api import configure_logger, create_dataset from gemseo.core.dataset import Dataset from gemseo.mlearning.api import create_regression_model from gemseo.mlearning.qual_measure.mse_measure import MSEMeasure configure_logger() standard_library.install_aliases() .. GENERATED FROM PYTHON SOURCE LINES 50-52 Define parameters ----------------- .. GENERATED FROM PYTHON SOURCE LINES 52-58 .. code-block:: default seed(12345) n_samples = 10 noise = 0.3 ** 2 max_pow = 5 amount_train = 0.8 .. GENERATED FROM PYTHON SOURCE LINES 59-62 Construct data -------------- We construct a parabola with added noise, on the interval [0, 1]. .. GENERATED FROM PYTHON SOURCE LINES 62-71 .. code-block:: default def f(x): return -4 * (x - 0.5) ** 2 + 3 x = linspace(0, 1, n_samples) y = f(x) + normal(0, noise, n_samples) .. GENERATED FROM PYTHON SOURCE LINES 72-74 Indices for test-train split ---------------------------- .. GENERATED FROM PYTHON SOURCE LINES 74-82 .. code-block:: default samples = arange(n_samples) n_train = int(amount_train * n_samples) n_test = n_samples - n_train train = sort(choice(samples, n_train, False)) test = sort([sample for sample in samples if sample not in train]) print("Train:", train) print("Test:", test) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none Train: [1 3 4 5 6 7 8 9] Test: [0 2] .. GENERATED FROM PYTHON SOURCE LINES 83-85 Build datasets -------------- .. GENERATED FROM PYTHON SOURCE LINES 85-91 .. code-block:: default data = hstack([x[:, None], y[:, None]]) variables = ["x", "y"] groups = {"x": Dataset.INPUT_GROUP, "y": Dataset.OUTPUT_GROUP} dataset = create_dataset("synthetic_data", data[train], variables, groups=groups) dataset_test = create_dataset("synthetic_data", data[test], variables, groups=groups) .. GENERATED FROM PYTHON SOURCE LINES 92-94 Build regression model ---------------------- .. GENERATED FROM PYTHON SOURCE LINES 94-97 .. code-block:: default model = create_regression_model("PolynomialRegression", dataset, degree=max_pow) print(model) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none PolynomialRegression(fit_intercept=True, penalty_level=0.0, l2_penalty_ratio=1.0, degree=5) | based on the scikit-learn library | built from 8 learning samples .. GENERATED FROM PYTHON SOURCE LINES 98-100 Predictions errors ------------------ .. GENERATED FROM PYTHON SOURCE LINES 100-108 .. code-block:: default measure = MSEMeasure(model) mse_train = measure.evaluate("learn") mse_test = measure.evaluate("test", test_data=dataset_test) print("Training error:", mse_train) print("Test error:", mse_test) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none Training error: [0.0003947] Test error: [2.29565983] .. GENERATED FROM PYTHON SOURCE LINES 109-111 Compute predictions ------------------- .. GENERATED FROM PYTHON SOURCE LINES 111-118 .. code-block:: default measure = MSEMeasure(model) model.learn() n_refined = 1000 x_refined = linspace(0, 1, n_refined) y_refined = model.predict({"x": x_refined[:, None]})["y"].flatten() .. GENERATED FROM PYTHON SOURCE LINES 119-121 Plot data points ---------------- .. GENERATED FROM PYTHON SOURCE LINES 121-126 .. code-block:: default plt.plot(x_refined, f(x_refined), label="Exact function") plt.scatter(x, y, label="Data points") plt.legend() plt.show() .. image:: /examples/mlearning/quality_measure/images/sphx_glr_plot_mse_001.png :alt: plot mse :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 127-129 Plot predictions ---------------- .. GENERATED FROM PYTHON SOURCE LINES 129-135 .. code-block:: default plt.plot(x_refined, y_refined, label="Prediction (x^{})".format(max_pow)) plt.scatter(x[train], y[train], label="Train") plt.scatter(x[test], y[test], color="r", label="Test") plt.legend() plt.show() .. image:: /examples/mlearning/quality_measure/images/sphx_glr_plot_mse_002.png :alt: plot mse :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 136-138 Compare different parameters ---------------------------- .. GENERATED FROM PYTHON SOURCE LINES 138-156 .. code-block:: default powers = [1, 2, 3, 4, 5, 7] test_errors = [] for power in powers: model = create_regression_model("PolynomialRegression", dataset, degree=power) measure = MSEMeasure(model) test_mse = measure.evaluate("test", test_data=dataset_test) test_errors += [test_mse] y_refined = model.predict({"x": x_refined[:, None]})["y"].flatten() plt.plot(x_refined, y_refined, label="x^{}".format(power)) plt.scatter(x[train], y[train], label="Train") plt.scatter(x[test], y[test], color="r", label="Test") plt.legend() plt.show() .. image:: /examples/mlearning/quality_measure/images/sphx_glr_plot_mse_003.png :alt: plot mse :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 157-158 Grid search .. GENERATED FROM PYTHON SOURCE LINES 158-160 .. code-block:: default print(test_errors) print("Power for minimal test error:", argmin(test_errors)) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none [array([0.54513687]), array([0.00518409]), array([0.00584647]), array([0.06387849]), array([2.29565983]), array([1.16961302])] Power for minimal test error: 1 .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.343 seconds) .. _sphx_glr_download_examples_mlearning_quality_measure_plot_mse.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_mse.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_mse.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_