Pushing the docs to dev/ for branch: master, commit 78a213b42c7437d806a6289372ad5411d2ee37ad

Author: sklearn-ci

dev/_downloads/0d59ba71a84b25ededa8e1298aed7cf2/plot_transformed_target.ipynb

@@ -6,35 +6,30 @@
 Effect of transforming the targets in regression model
 ======================================================
 
-In this example, we give an overview of the
-:class:`sklearn.compose.TransformedTargetRegressor`. Two examples
-illustrate the benefit of transforming the targets before learning a linear
+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 Boston housing data set.
-
+example is based on the Ames housing data set.
 """
 
 # Author: Guillaume Lemaitre <[email protected]>
 # License: BSD 3 clause
 
-
 import numpy as np
 import matplotlib
 import matplotlib.pyplot as plt
 from distutils.version import LooseVersion
 
-print(__doc__)
-
-###############################################################################
-# Synthetic example
-###############################################################################
-
 from sklearn.datasets import make_regression
 from sklearn.model_selection import train_test_split
 from sklearn.linear_model import RidgeCV
 from sklearn.compose import TransformedTargetRegressor
 from sklearn.metrics import median_absolute_error, r2_score
 
+###############################################################################
+# Synthetic example
+##############################################################################
 
 # `normed` is being deprecated in favor of `density` in histograms
 if LooseVersion(matplotlib.__version__) >= '2.1':
@@ -43,21 +38,24 @@
     density_param = {'normed': True}
 
 ###############################################################################
-# A synthetic random regression problem is generated. The targets ``y`` are
-# modified by: (i) translating all targets such that all entries are
-# non-negative and (ii) applying an exponential function to obtain non-linear
-# targets which cannot be fitted using a simple linear model.
+# 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.
 
 X, y = make_regression(n_samples=10000, noise=100, random_state=0)
-y = np.exp((y + abs(y.min())) / 200)
+y = np.expm1((y + abs(y.min())) / 200)
 y_trans = np.log1p(y)
 
 ###############################################################################
-# The following illustrate the probability density functions of the target
+# Below we plot the probability density functions of the target
 # before and after applying the logarithmic functions.
 
 f, (ax0, ax1) = plt.subplots(1, 2)
@@ -73,24 +71,24 @@
 ax1.set_xlabel('Target')
 ax1.set_title('Transformed target distribution')
 
-f.suptitle("Synthetic data", y=0.035)
+f.suptitle("Synthetic data", y=0.06, x=0.53)
 f.tight_layout(rect=[0.05, 0.05, 0.95, 0.95])
 
 X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)
 
 ###############################################################################
 # 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 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 (MAE).
 
 f, (ax0, ax1) = plt.subplots(1, 2, sharey=True)
-
+# Use linear model
 regr = RidgeCV()
 regr.fit(X_train, y_train)
 y_pred = regr.predict(X_test)
-
+# Plot results
 ax0.scatter(y_test, y_pred)
 ax0.plot([0, 2000], [0, 2000], '--k')
 ax0.set_ylabel('Target predicted')
@@ -100,7 +98,7 @@
     r2_score(y_test, y_pred), median_absolute_error(y_test, y_pred)))
 ax0.set_xlim([0, 2000])
 ax0.set_ylim([0, 2000])
-
+# Transform targets and use same linear model
 regr_trans = TransformedTargetRegressor(regressor=RidgeCV(),
                                         func=np.log1p,
                                         inverse_func=np.expm1)
@@ -125,83 +123,103 @@
 ###############################################################################
 
 ###############################################################################
-# In a similar manner, the boston housing data set is used to show the impact
+# 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
-# targets to be predicted corresponds to the weighted distances to the five
-# Boston employment centers.
+# target to be predicted is the selling price of each house.
 
-from sklearn.datasets import load_boston
+from sklearn.datasets import fetch_openml
 from sklearn.preprocessing import QuantileTransformer, quantile_transform
 
-dataset = load_boston()
-target = np.array(dataset.feature_names) == "DIS"
-X = dataset.data[:, np.logical_not(target)]
-y = dataset.data[:, target].squeeze()
-y_trans = quantile_transform(dataset.data[:, target],
-                             n_quantiles=300,
+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'])
+y = ames.target
+y_trans = quantile_transform(y.to_frame(),
+                             n_quantiles=900,
                              output_distribution='normal',
                              copy=True).squeeze()
 
 ###############################################################################
-# A :class:`sklearn.preprocessing.QuantileTransformer` is used such that the
-# targets follows a normal distribution before applying a
-# :class:`sklearn.linear_model.RidgeCV` model.
+# A :class:`~sklearn.preprocessing.QuantileTransformer` is used to normalize
+# the target distribution before applying a
+# :class:`~sklearn.linear_model.RidgeCV` model.
 
 f, (ax0, ax1) = plt.subplots(1, 2)
 
 ax0.hist(y, bins=100, **density_param)
 ax0.set_ylabel('Probability')
 ax0.set_xlabel('Target')
-ax0.set_title('Target distribution')
+ax0.text(s='Target distribution', x=1.2e5, y=9.8e-6, fontsize=12)
+ax0.ticklabel_format(axis="both", style="sci", scilimits=(0, 0))
 
 ax1.hist(y_trans, bins=100, **density_param)
 ax1.set_ylabel('Probability')
 ax1.set_xlabel('Target')
-ax1.set_title('Transformed target distribution')
+ax1.text(s='Transformed target distribution', x=-6.8, y=0.479, fontsize=12)
 
-f.suptitle("Boston housing data: distance to employment centers", y=0.035)
+f.suptitle("Ames housing data: selling price", y=0.04)
 f.tight_layout(rect=[0.05, 0.05, 0.95, 0.95])
 
 X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)
 
 ###############################################################################
 # The effect of the transformer is weaker than on the synthetic data. However,
-# the transform induces a decrease of the MAE.
+# the transformation results in an increase in :math:`R^2` and large decrease
+# of the MAE. 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.
 
-f, (ax0, ax1) = plt.subplots(1, 2, sharey=True)
+f, (ax0, ax1) = plt.subplots(2, 2, sharey='row', figsize=(6.5, 8))
 
 regr = RidgeCV()
 regr.fit(X_train, y_train)
 y_pred = regr.predict(X_test)
 
-ax0.scatter(y_test, y_pred)
-ax0.plot([0, 10], [0, 10], '--k')
-ax0.set_ylabel('Target predicted')
-ax0.set_xlabel('True Target')
-ax0.set_title('Ridge regression \n without target transformation')
-ax0.text(1, 9, r'$R^2$=%.2f, MAE=%.2f' % (
+ax0[0].scatter(y_pred, y_test, s=8)
+ax0[0].plot([0, 7e5], [0, 7e5], '--k')
+ax0[0].set_ylabel('True target')
+ax0[0].set_xlabel('Predicted target')
+ax0[0].text(s='Ridge regression \n without target transformation', x=-5e4,
+            y=8e5, fontsize=12, multialignment='center')
+ax0[0].text(3e4, 64e4, r'$R^2$=%.2f, MAE=%.2f' % (
     r2_score(y_test, y_pred), median_absolute_error(y_test, y_pred)))
-ax0.set_xlim([0, 10])
-ax0.set_ylim([0, 10])
+ax0[0].set_xlim([0, 7e5])
+ax0[0].set_ylim([0, 7e5])
+ax0[0].ticklabel_format(axis="both", style="sci", scilimits=(0, 0))
+
+ax1[0].scatter(y_pred, (y_pred - y_test), s=8)
+ax1[0].set_ylabel('Residual')
+ax1[0].set_xlabel('Predicted target')
+ax1[0].ticklabel_format(axis="both", style="sci", scilimits=(0, 0))
 
 regr_trans = TransformedTargetRegressor(
     regressor=RidgeCV(),
-    transformer=QuantileTransformer(n_quantiles=300,
+    transformer=QuantileTransformer(n_quantiles=900,
                                     output_distribution='normal'))
 regr_trans.fit(X_train, y_train)
 y_pred = regr_trans.predict(X_test)
 
-ax1.scatter(y_test, y_pred)
-ax1.plot([0, 10], [0, 10], '--k')
-ax1.set_ylabel('Target predicted')
-ax1.set_xlabel('True Target')
-ax1.set_title('Ridge regression \n with target transformation')
-ax1.text(1, 9, r'$R^2$=%.2f, MAE=%.2f' % (
+ax0[1].scatter(y_pred, y_test, s=8)
+ax0[1].plot([0, 7e5], [0, 7e5], '--k')
+ax0[1].set_ylabel('True target')
+ax0[1].set_xlabel('Predicted target')
+ax0[1].text(s='Ridge regression \n with target transformation', x=-5e4,
+            y=8e5, fontsize=12, multialignment='center')
+ax0[1].text(3e4, 64e4, r'$R^2$=%.2f, MAE=%.2f' % (
     r2_score(y_test, y_pred), median_absolute_error(y_test, y_pred)))
-ax1.set_xlim([0, 10])
-ax1.set_ylim([0, 10])
+ax0[1].set_xlim([0, 7e5])
+ax0[1].set_ylim([0, 7e5])
+ax0[1].ticklabel_format(axis="both", style="sci", scilimits=(0, 0))
 
-f.suptitle("Boston housing data: distance to employment centers", y=0.035)
-f.tight_layout(rect=[0.05, 0.05, 0.95, 0.95])
+ax1[1].scatter(y_pred, (y_pred - y_test), s=8)
+ax1[1].set_ylabel('Residual')
+ax1[1].set_xlabel('Predicted target')
+ax1[1].ticklabel_format(axis="both", style="sci", scilimits=(0, 0))
+
+f.suptitle("Ames housing data: selling price", y=0.035)
 
 plt.show()