.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/compose/plot_transformed_target.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 JupyterLite or Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_compose_plot_transformed_target.py: ====================================================== Effect of transforming the targets in regression model ====================================================== In this example, we give an overview of :class:`~sklearn.compose.TransformedTargetRegressor`. We use two examples to illustrate the benefit of transforming the targets before learning a linear regression model. The first example uses synthetic data while the second example is based on the Ames housing data set. .. GENERATED FROM PYTHON SOURCE LINES 13-19 .. code-block:: Python # Author: Guillaume Lemaitre # License: BSD 3 clause print(__doc__) .. GENERATED FROM PYTHON SOURCE LINES 20-34 Synthetic example ################## A synthetic random regression dataset is generated. The targets ``y`` are modified by: 1. translating all targets such that all entries are non-negative (by adding the absolute value of the lowest ``y``) and 2. applying an exponential function to obtain non-linear targets which cannot be fitted using a simple linear model. Therefore, a logarithmic (`np.log1p`) and an exponential function (`np.expm1`) will be used to transform the targets before training a linear regression model and using it for prediction. .. GENERATED FROM PYTHON SOURCE LINES 34-42 .. code-block:: Python import numpy as np from sklearn.datasets import make_regression X, y = make_regression(n_samples=10_000, noise=100, random_state=0) y = np.expm1((y + abs(y.min())) / 200) y_trans = np.log1p(y) .. GENERATED FROM PYTHON SOURCE LINES 43-45 Below we plot the probability density functions of the target before and after applying the logarithmic functions. .. GENERATED FROM PYTHON SOURCE LINES 45-67 .. code-block:: Python import matplotlib.pyplot as plt from sklearn.model_selection import train_test_split f, (ax0, ax1) = plt.subplots(1, 2) ax0.hist(y, bins=100, density=True) ax0.set_xlim([0, 2000]) ax0.set_ylabel("Probability") ax0.set_xlabel("Target") ax0.set_title("Target distribution") ax1.hist(y_trans, bins=100, density=True) ax1.set_ylabel("Probability") ax1.set_xlabel("Target") ax1.set_title("Transformed target distribution") f.suptitle("Synthetic data", y=1.05) plt.tight_layout() X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0) .. image-sg:: /auto_examples/compose/images/sphx_glr_plot_transformed_target_001.png :alt: Synthetic data, Target distribution, Transformed target distribution :srcset: /auto_examples/compose/images/sphx_glr_plot_transformed_target_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 68-73 At first, a linear model will be applied on the original targets. Due to the non-linearity, the model trained will not be precise during prediction. Subsequently, a logarithmic function is used to linearize the targets, allowing better prediction even with a similar linear model as reported by the median absolute error (MedAE). .. GENERATED FROM PYTHON SOURCE LINES 73-83 .. code-block:: Python from sklearn.metrics import median_absolute_error, r2_score def compute_score(y_true, y_pred): return { "R2": f"{r2_score(y_true, y_pred):.3f}", "MedAE": f"{median_absolute_error(y_true, y_pred):.3f}", } .. GENERATED FROM PYTHON SOURCE LINES 84-124 .. code-block:: Python from sklearn.compose import TransformedTargetRegressor from sklearn.linear_model import RidgeCV from sklearn.metrics import PredictionErrorDisplay f, (ax0, ax1) = plt.subplots(1, 2, sharey=True) ridge_cv = RidgeCV().fit(X_train, y_train) y_pred_ridge = ridge_cv.predict(X_test) ridge_cv_with_trans_target = TransformedTargetRegressor( regressor=RidgeCV(), func=np.log1p, inverse_func=np.expm1 ).fit(X_train, y_train) y_pred_ridge_with_trans_target = ridge_cv_with_trans_target.predict(X_test) PredictionErrorDisplay.from_predictions( y_test, y_pred_ridge, kind="actual_vs_predicted", ax=ax0, scatter_kwargs={"alpha": 0.5}, ) PredictionErrorDisplay.from_predictions( y_test, y_pred_ridge_with_trans_target, kind="actual_vs_predicted", ax=ax1, scatter_kwargs={"alpha": 0.5}, ) # Add the score in the legend of each axis for ax, y_pred in zip([ax0, ax1], [y_pred_ridge, y_pred_ridge_with_trans_target]): for name, score in compute_score(y_test, y_pred).items(): ax.plot([], [], " ", label=f"{name}={score}") ax.legend(loc="upper left") ax0.set_title("Ridge regression \n without target transformation") ax1.set_title("Ridge regression \n with target transformation") f.suptitle("Synthetic data", y=1.05) plt.tight_layout() .. image-sg:: /auto_examples/compose/images/sphx_glr_plot_transformed_target_002.png :alt: Synthetic data, Ridge regression without target transformation, Ridge regression with target transformation :srcset: /auto_examples/compose/images/sphx_glr_plot_transformed_target_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 125-131 Real-world data set #################### In a similar manner, the Ames housing data set is used to show the impact of transforming the targets before learning a model. In this example, the target to be predicted is the selling price of each house. .. GENERATED FROM PYTHON SOURCE LINES 131-145 .. code-block:: Python from sklearn.datasets import fetch_openml from sklearn.preprocessing import quantile_transform ames = fetch_openml(name="house_prices", as_frame=True) # Keep only numeric columns X = ames.data.select_dtypes(np.number) # Remove columns with NaN or Inf values X = X.drop(columns=["LotFrontage", "GarageYrBlt", "MasVnrArea"]) # Let the price be in k$ y = ames.target / 1000 y_trans = quantile_transform( y.to_frame(), n_quantiles=900, output_distribution="normal", copy=True ).squeeze() .. GENERATED FROM PYTHON SOURCE LINES 146-149 A :class:`~sklearn.preprocessing.QuantileTransformer` is used to normalize the target distribution before applying a :class:`~sklearn.linear_model.RidgeCV` model. .. GENERATED FROM PYTHON SOURCE LINES 149-164 .. code-block:: Python f, (ax0, ax1) = plt.subplots(1, 2) ax0.hist(y, bins=100, density=True) ax0.set_ylabel("Probability") ax0.set_xlabel("Target") ax0.set_title("Target distribution") ax1.hist(y_trans, bins=100, density=True) ax1.set_ylabel("Probability") ax1.set_xlabel("Target") ax1.set_title("Transformed target distribution") f.suptitle("Ames housing data: selling price", y=1.05) plt.tight_layout() .. image-sg:: /auto_examples/compose/images/sphx_glr_plot_transformed_target_003.png :alt: Ames housing data: selling price, Target distribution, Transformed target distribution :srcset: /auto_examples/compose/images/sphx_glr_plot_transformed_target_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 165-167 .. code-block:: Python X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1) .. GENERATED FROM PYTHON SOURCE LINES 168-175 The effect of the transformer is weaker than on the synthetic data. However, the transformation results in an increase in :math:`R^2` and large decrease of the MedAE. The residual plot (predicted target - true target vs predicted target) without target transformation takes on a curved, 'reverse smile' shape due to residual values that vary depending on the value of predicted target. With target transformation, the shape is more linear indicating better model fit. .. GENERATED FROM PYTHON SOURCE LINES 175-234 .. code-block:: Python from sklearn.preprocessing import QuantileTransformer f, (ax0, ax1) = plt.subplots(2, 2, sharey="row", figsize=(6.5, 8)) ridge_cv = RidgeCV().fit(X_train, y_train) y_pred_ridge = ridge_cv.predict(X_test) ridge_cv_with_trans_target = TransformedTargetRegressor( regressor=RidgeCV(), transformer=QuantileTransformer(n_quantiles=900, output_distribution="normal"), ).fit(X_train, y_train) y_pred_ridge_with_trans_target = ridge_cv_with_trans_target.predict(X_test) # plot the actual vs predicted values PredictionErrorDisplay.from_predictions( y_test, y_pred_ridge, kind="actual_vs_predicted", ax=ax0[0], scatter_kwargs={"alpha": 0.5}, ) PredictionErrorDisplay.from_predictions( y_test, y_pred_ridge_with_trans_target, kind="actual_vs_predicted", ax=ax0[1], scatter_kwargs={"alpha": 0.5}, ) # Add the score in the legend of each axis for ax, y_pred in zip([ax0[0], ax0[1]], [y_pred_ridge, y_pred_ridge_with_trans_target]): for name, score in compute_score(y_test, y_pred).items(): ax.plot([], [], " ", label=f"{name}={score}") ax.legend(loc="upper left") ax0[0].set_title("Ridge regression \n without target transformation") ax0[1].set_title("Ridge regression \n with target transformation") # plot the residuals vs the predicted values PredictionErrorDisplay.from_predictions( y_test, y_pred_ridge, kind="residual_vs_predicted", ax=ax1[0], scatter_kwargs={"alpha": 0.5}, ) PredictionErrorDisplay.from_predictions( y_test, y_pred_ridge_with_trans_target, kind="residual_vs_predicted", ax=ax1[1], scatter_kwargs={"alpha": 0.5}, ) ax1[0].set_title("Ridge regression \n without target transformation") ax1[1].set_title("Ridge regression \n with target transformation") f.suptitle("Ames housing data: selling price", y=1.05) plt.tight_layout() plt.show() .. image-sg:: /auto_examples/compose/images/sphx_glr_plot_transformed_target_004.png :alt: Ames housing data: selling price, Ridge regression without target transformation, Ridge regression with target transformation, Ridge regression without target transformation, Ridge regression with target transformation :srcset: /auto_examples/compose/images/sphx_glr_plot_transformed_target_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.451 seconds) .. _sphx_glr_download_auto_examples_compose_plot_transformed_target.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/compose/plot_transformed_target.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/?path=auto_examples/compose/plot_transformed_target.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_transformed_target.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_transformed_target.py ` .. include:: plot_transformed_target.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_