.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "gen_notes/01_missing_values.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_gen_notes_01_missing_values.py: ========================================= Machine learning with missing values ========================================= Here we use simulated data to understanding the fundamentals of statistical learning with missing values. This notebook reveals why a HistGradientBoostingRegressor ( :class:`sklearn.ensemble.HistGradientBoostingRegressor` ) is a good choice to predict with missing values. We use simulations to control the missing-value mechanism, and inspect it's impact on predictive models. In particular, standard imputation procedures can reconstruct missing values without distortion only if the data is *missing at random*. A good introduction to the mathematics behind this notebook can be found in https://arxiv.org/abs/1902.06931 .. topic:: **Missing values in categorical data** If a categorical column has missing values, the simplest approach is to create a specific category "missing" and assign missing values to this new category, to represent missingness in the classifier. Indeed, as we will see, imputation is not crucial for prediction. In the following we focus on continuous columns, where the discrete nature of a missing value poses more problems. .. GENERATED FROM PYTHON SOURCE LINES 34-43 The fully-observed data: a toy regression problem ================================================== We consider a simple regression problem where X (the data) is bivariate gaussian, and y (the prediction target) is a linear function of the first coordinate, with noise. The data-generating mechanism ------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 43-58 .. code-block:: default import numpy as np def generate_without_missing_values(n_samples, rng=42): mean = [0, 0] cov = [[1, 0.9], [0.9, 1]] if not isinstance(rng, np.random.RandomState): rng = np.random.RandomState(rng) X = rng.multivariate_normal(mean, cov, size=n_samples) epsilon = 0.1 * rng.randn(n_samples) y = X[:, 0] + epsilon return X, y .. GENERATED FROM PYTHON SOURCE LINES 59-60 A quick plot reveals what the data looks like .. GENERATED FROM PYTHON SOURCE LINES 60-69 .. code-block:: default import matplotlib.pyplot as plt plt.rcParams['figure.figsize'] = (5, 4) # Smaller default figure size plt.figure() X_full, y_full = generate_without_missing_values(1000) plt.scatter(X_full[:, 0], X_full[:, 1], c=y_full) plt.colorbar(label='y') .. image-sg:: /gen_notes/images/sphx_glr_01_missing_values_001.png :alt: 01 missing values :srcset: /gen_notes/images/sphx_glr_01_missing_values_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 70-79 Missing completely at random settings ====================================== We now consider missing completely at random settings (a special case of missing at random): the missingness is completely independent from the values. The missing-values mechanism ----------------------------- .. GENERATED FROM PYTHON SOURCE LINES 79-90 .. code-block:: default def generate_mcar(n_samples, missing_rate=.5, rng=42): X, y = generate_without_missing_values(n_samples, rng=rng) if not isinstance(rng, np.random.RandomState): rng = np.random.RandomState(rng) M = rng.binomial(1, missing_rate, (n_samples, 2)) np.putmask(X, M, np.nan) return X, y .. GENERATED FROM PYTHON SOURCE LINES 91-92 A quick plot to look at the data .. GENERATED FROM PYTHON SOURCE LINES 92-100 .. code-block:: default X, y = generate_mcar(500) plt.figure() plt.scatter(X_full[:, 0], X_full[:, 1], color='.8', ec='.5', label='All data') plt.colorbar(label='y') plt.scatter(X[:, 0], X[:, 1], c=y, label='Fully observed') plt.legend() .. image-sg:: /gen_notes/images/sphx_glr_01_missing_values_002.png :alt: 01 missing values :srcset: /gen_notes/images/sphx_glr_01_missing_values_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 101-112 We can see that the distribution of the fully-observed data is the same than that of the original data Conditional Imputation with the IterativeImputer ------------------------------------------------ As the data is MAR (missing at random), an imputer can use the conditional dependencies between the observed and the missing values to impute the missing values. We'll use the IterativeImputer, a good imputer, but it needs to be enabled .. GENERATED FROM PYTHON SOURCE LINES 112-116 .. code-block:: default from sklearn.experimental import enable_iterative_imputer from sklearn import impute iterative_imputer = impute.IterativeImputer() .. GENERATED FROM PYTHON SOURCE LINES 117-121 Let us try the imputer on the small data used to visualize **The imputation is learned by fitting the imputer on the data with missing values** .. GENERATED FROM PYTHON SOURCE LINES 121-123 .. code-block:: default iterative_imputer.fit(X) .. raw:: html 
IterativeImputer()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.


.. GENERATED FROM PYTHON SOURCE LINES 124-125 **The data are imputed with the transform method** .. GENERATED FROM PYTHON SOURCE LINES 125-127 .. code-block:: default X_imputed = iterative_imputer.transform(X) .. GENERATED FROM PYTHON SOURCE LINES 128-129 We can display the imputed data as our previous visualization .. GENERATED FROM PYTHON SOURCE LINES 129-137 .. code-block:: default plt.figure() plt.scatter(X_full[:, 0], X_full[:, 1], color='.8', ec='.5', label='All data', alpha=.5) plt.scatter(X_imputed[:, 0], X_imputed[:, 1], c=y, marker='X', label='Imputed') plt.colorbar(label='y') plt.legend() .. image-sg:: /gen_notes/images/sphx_glr_01_missing_values_003.png :alt: 01 missing values :srcset: /gen_notes/images/sphx_glr_01_missing_values_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 138-150 We can see that the imputer did a fairly good job of recovering the data distribution Supervised learning: imputation and a linear model ----------------------------------------------------------- Given that the relationship between the fully-observed X and y is a linear relationship, it seems natural to use a linear model for prediction. It must be adapted to missing values using imputation. To use it in supervised setting, we will pipeline it with a linear model, using a ridge, which is a good default linear model .. GENERATED FROM PYTHON SOURCE LINES 150-155 .. code-block:: default from sklearn.pipeline import make_pipeline from sklearn.linear_model import RidgeCV iterative_and_ridge = make_pipeline(impute.IterativeImputer(), RidgeCV()) .. GENERATED FROM PYTHON SOURCE LINES 156-159 We can evaluate the model performance in a cross-validation loop (for better evaluation accuracy, we increase slightly the number of folds to 10) .. GENERATED FROM PYTHON SOURCE LINES 159-165 .. code-block:: default from sklearn import model_selection scores_iterative_and_ridge = model_selection.cross_val_score( iterative_and_ridge, X, y, cv=10) scores_iterative_and_ridge .. rst-class:: sphx-glr-script-out .. code-block:: none array([0.61639853, 0.5814862 , 0.70136887, 0.64571923, 0.58785589, 0.79618649, 0.65278055, 0.8454113 , 0.81722841, 0.76948479]) .. GENERATED FROM PYTHON SOURCE LINES 166-169 **Computational cost**: One drawback of the IterativeImputer to keep in mind is that its computational cost can become prohibitive of large datasets (it has a bad computation scalability). .. GENERATED FROM PYTHON SOURCE LINES 171-175 Mean imputation: SimpleImputer ------------------------------- We can try a simple imputer: imputation by the mean .. GENERATED FROM PYTHON SOURCE LINES 175-177 .. code-block:: default mean_imputer = impute.SimpleImputer() .. GENERATED FROM PYTHON SOURCE LINES 178-179 A quick visualization reveals a larger disortion of the distribution .. GENERATED FROM PYTHON SOURCE LINES 179-187 .. code-block:: default X_imputed = mean_imputer.fit_transform(X) plt.figure() plt.scatter(X_full[:, 0], X_full[:, 1], color='.8', ec='.5', label='All data', alpha=.5) plt.scatter(X_imputed[:, 0], X_imputed[:, 1], c=y, marker='X', label='Imputed') plt.colorbar(label='y') .. image-sg:: /gen_notes/images/sphx_glr_01_missing_values_004.png :alt: 01 missing values :srcset: /gen_notes/images/sphx_glr_01_missing_values_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 188-189 Evaluating in prediction pipeline .. GENERATED FROM PYTHON SOURCE LINES 189-195 .. code-block:: default mean_and_ridge = make_pipeline(impute.SimpleImputer(), RidgeCV()) scores_mean_and_ridge = model_selection.cross_val_score( mean_and_ridge, X, y, cv=10) scores_mean_and_ridge .. rst-class:: sphx-glr-script-out .. code-block:: none array([0.58596256, 0.55215184, 0.61081314, 0.55282029, 0.54053836, 0.64325051, 0.60147921, 0.84188079, 0.68152965, 0.67441335]) .. GENERATED FROM PYTHON SOURCE LINES 196-201 Supervised learning without imputation ---------------------------------------- The HistGradientBoosting models are based on trees, which can be adapted to model directly missing values .. GENERATED FROM PYTHON SOURCE LINES 201-208 .. code-block:: default from sklearn.experimental import enable_hist_gradient_boosting from sklearn.ensemble import HistGradientBoostingRegressor score_hist_gradient_boosting = model_selection.cross_val_score( HistGradientBoostingRegressor(), X, y, cv=10) score_hist_gradient_boosting .. rst-class:: sphx-glr-script-out .. code-block:: none /home/varoquau/dev/scikit-learn/sklearn/experimental/enable_hist_gradient_boosting.py:15: UserWarning: Since version 1.0, it is not needed to import enable_hist_gradient_boosting anymore. HistGradientBoostingClassifier and HistGradientBoostingRegressor are now stable and can be normally imported from sklearn.ensemble. warnings.warn( array([0.61170698, 0.56911116, 0.635685 , 0.62752111, 0.58094569, 0.71569692, 0.62359162, 0.83829684, 0.81283438, 0.74080482]) .. GENERATED FROM PYTHON SOURCE LINES 209-213 Recap: which pipeline predicts well on our small data? ------------------------------------------------------- Let's plot the scores to see things better .. GENERATED FROM PYTHON SOURCE LINES 213-227 .. code-block:: default import pandas as pd import seaborn as sns scores = pd.DataFrame({'Mean imputation + Ridge': scores_mean_and_ridge, 'IterativeImputer + Ridge': scores_iterative_and_ridge, 'HistGradientBoostingRegressor': score_hist_gradient_boosting, }) sns.boxplot(data=scores, orient='h') plt.title('Prediction accuracy\n linear and small data\n' 'Missing Completely at Random') plt.tight_layout() .. image-sg:: /gen_notes/images/sphx_glr_01_missing_values_005.png :alt: Prediction accuracy linear and small data Missing Completely at Random :srcset: /gen_notes/images/sphx_glr_01_missing_values_005.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 228-235 Not much difference with the more sophisticated imputer. A more thorough analysis would be necessary, with more cross-validation runs. Prediction performance with large datasets ------------------------------------------- Let us compare models in regimes where there is plenty of data .. GENERATED FROM PYTHON SOURCE LINES 235-238 .. code-block:: default X, y = generate_mcar(n_samples=20000) .. GENERATED FROM PYTHON SOURCE LINES 239-240 Iterative imputation and linear model .. GENERATED FROM PYTHON SOURCE LINES 240-243 .. code-block:: default scores_iterative_and_ridge= model_selection.cross_val_score( iterative_and_ridge, X, y, cv=10) .. GENERATED FROM PYTHON SOURCE LINES 244-245 Mean imputation and linear model .. GENERATED FROM PYTHON SOURCE LINES 245-248 .. code-block:: default scores_mean_and_ridge = model_selection.cross_val_score( mean_and_ridge, X, y, cv=10) .. GENERATED FROM PYTHON SOURCE LINES 249-251 And now the HistGradientBoostingRegressor, which does not need imputation .. GENERATED FROM PYTHON SOURCE LINES 251-254 .. code-block:: default score_hist_gradient_boosting = model_selection.cross_val_score( HistGradientBoostingRegressor(), X, y, cv=10) .. GENERATED FROM PYTHON SOURCE LINES 255-256 We plot the results .. GENERATED FROM PYTHON SOURCE LINES 256-267 .. code-block:: default scores = pd.DataFrame({'Mean imputation + Ridge': scores_mean_and_ridge, 'IterativeImputer + Ridge': scores_iterative_and_ridge, 'HistGradientBoostingRegressor': score_hist_gradient_boosting, }) sns.boxplot(data=scores, orient='h') plt.title('Prediction accuracy\n linear and large data\n' 'Missing Completely at Random') plt.tight_layout() .. image-sg:: /gen_notes/images/sphx_glr_01_missing_values_006.png :alt: Prediction accuracy linear and large data Missing Completely at Random :srcset: /gen_notes/images/sphx_glr_01_missing_values_006.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 268-281 **When there is a reasonnable amout of data, the HistGradientBoostingRegressor is the best strategy** even for a linear data-generating mechanism, in MAR settings, which are settings favorable to imputation + linear model [#]_. .. [#] Even in the case of a linear data-generating mechanism, the optimal prediction one data imputed by a constant is a piecewise affine function with 2^d regions ( http://proceedings.mlr.press/v108/morvan20a.html ). The larger the dimensionality (number of features), the more a imperfect imputation is hard to approximate with a simple model. | .. GENERATED FROM PYTHON SOURCE LINES 284-293 Missing not at random: censoring ====================================== We now consider missing not at random settings, in particular self-masking or censoring, where large values are more likely to be missing. The missing-values mechanism ----------------------------- .. GENERATED FROM PYTHON SOURCE LINES 293-306 .. code-block:: default def generate_censored(n_samples, missing_rate=.4, rng=42): X, y = generate_without_missing_values(n_samples, rng=rng) if not isinstance(rng, np.random.RandomState): rng = np.random.RandomState(rng) B = rng.binomial(1, 2 * missing_rate, (n_samples, 2)) M = (X > 0.5) * B np.putmask(X, M, np.nan) return X, y .. GENERATED FROM PYTHON SOURCE LINES 307-308 A quick plot to look at the data .. GENERATED FROM PYTHON SOURCE LINES 308-317 .. code-block:: default X, y = generate_censored(500, missing_rate=.4) plt.figure() plt.scatter(X_full[:, 0], X_full[:, 1], color='.8', ec='.5', label='All data') plt.colorbar(label='y') plt.scatter(X[:, 0], X[:, 1], c=y, label='Fully observed') plt.legend() .. image-sg:: /gen_notes/images/sphx_glr_01_missing_values_007.png :alt: 01 missing values :srcset: /gen_notes/images/sphx_glr_01_missing_values_007.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 318-320 Here the full-observed data does not reflect well at all the distribution of all the data .. GENERATED FROM PYTHON SOURCE LINES 322-327 Imputation fails to recover the distribution -------------------------------------------------------- With MNAR data, off-the-shelf imputation methods do not recover the initial distribution: .. GENERATED FROM PYTHON SOURCE LINES 327-339 .. code-block:: default iterative_imputer = impute.IterativeImputer() X_imputed = iterative_imputer.fit_transform(X) plt.figure() plt.scatter(X_full[:, 0], X_full[:, 1], color='.8', ec='.5', label='All data', alpha=.5) plt.scatter(X_imputed[:, 0], X_imputed[:, 1], c=y, marker='X', label='Imputed') plt.colorbar(label='y') plt.legend() .. image-sg:: /gen_notes/images/sphx_glr_01_missing_values_008.png :alt: 01 missing values :srcset: /gen_notes/images/sphx_glr_01_missing_values_008.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 340-358 Recovering the initial data distribution would need much more mass on the right and the top of the figure. The imputed data is shifted to lower values than the original data. Note also that as imputed values typically have lower X values than their full-observed counterparts, the association between X and y is also distorted. This is visible as the imputed values appear as lighter diagonal lines. An important consequence is that **the link between imputed X and y is no longer linear**, although the original data-generating mechanism is linear [#]_. For this reason, **it is often a good idea to use non-linear learners in the presence of missing values**. .. [#] As mentionned above, even in the case of a linear data-generating mechanism, imperfect imputation leads to complex functions to link to y ( http://proceedings.mlr.press/v108/morvan20a.html ) .. GENERATED FROM PYTHON SOURCE LINES 360-364 Predictive pipelines ----------------------------- Let us now evaluate predictive pipelines .. GENERATED FROM PYTHON SOURCE LINES 364-397 .. code-block:: default scores = dict() # Iterative imputation and linear model scores['IterativeImputer + Ridge'] = model_selection.cross_val_score( iterative_and_ridge, X, y, cv=10) # Mean imputation and linear model scores['Mean imputation + Ridge'] = model_selection.cross_val_score( mean_and_ridge, X, y, cv=10) # IterativeImputer and non-linear model iterative_and_gb = make_pipeline(impute.SimpleImputer(), HistGradientBoostingRegressor()) scores['Mean imputation\n+ HistGradientBoostingRegressor'] = model_selection.cross_val_score( iterative_and_gb, X, y, cv=10) # Mean imputation and non-linear model mean_and_gb = make_pipeline(impute.SimpleImputer(), HistGradientBoostingRegressor()) scores['IterativeImputer\n+ HistGradientBoostingRegressor'] = model_selection.cross_val_score( mean_and_gb, X, y, cv=10) # And now the HistGradientBoostingRegressor, whithout imputation scores['HistGradientBoostingRegressor'] = model_selection.cross_val_score( HistGradientBoostingRegressor(), X, y, cv=10) # We plot the results sns.boxplot(data=pd.DataFrame(scores), orient='h') plt.title('Prediction accuracy\n linear and small data\n' 'Missing not at Random') plt.tight_layout() .. image-sg:: /gen_notes/images/sphx_glr_01_missing_values_009.png :alt: Prediction accuracy linear and small data Missing not at Random :srcset: /gen_notes/images/sphx_glr_01_missing_values_009.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 398-406 We can see that the imputation is not the most important step of the pipeline [#]_, rather **what is important is to use a powerful model**. Here there is information in missingness (if a value is missing, it is large), information that a model can use to predict better. .. [#] Note that there are less missing values in the example here compared to the section above on MCAR, hence the absolute prediction accuracies are not comparable. .. GENERATED FROM PYTHON SOURCE LINES 408-414 .. topic:: Prediction with missing values The data above are very simple: linear data-generating mechanism, Gaussian, and low dimensional. Yet, they show the importance of using non-linear models, in particular the HistGradientBoostingRegressor which natively deals with missing values. .. GENERATED FROM PYTHON SOURCE LINES 417-422 Using a predictor for the fully-observed case ============================================== Let us go back to the "easy" case of the missing completely at random settings with plenty of data .. GENERATED FROM PYTHON SOURCE LINES 422-426 .. code-block:: default n_samples = 20000 X, y = generate_mcar(n_samples, missing_rate=.5) .. GENERATED FROM PYTHON SOURCE LINES 427-429 Suppose we have been able to train a predictive model that works on fully-observed data: .. GENERATED FROM PYTHON SOURCE LINES 429-436 .. code-block:: default X_full, y_full = generate_without_missing_values(n_samples) full_data_predictor = HistGradientBoostingRegressor() full_data_predictor.fit(X_full, y_full) model_selection.cross_val_score(full_data_predictor, X_full, y_full) .. rst-class:: sphx-glr-script-out .. code-block:: none array([0.98934188, 0.9897668 , 0.98932951, 0.98916616, 0.98898611]) .. GENERATED FROM PYTHON SOURCE LINES 437-440 The cross validation reveals that the predictor achieves an excellent explained variance; it is a near-perfect predictor on fully observed data .. GENERATED FROM PYTHON SOURCE LINES 442-445 Now we turn to data with missing values. Given that our data is MAR (missing at random), we will use imputation to build a completed data that looks like the full-observed data .. GENERATED FROM PYTHON SOURCE LINES 445-449 .. code-block:: default iterative_imputer = impute.IterativeImputer() X_imputed = iterative_imputer.fit_transform(X) .. GENERATED FROM PYTHON SOURCE LINES 450-451 The full data predictor can be used on the imputed data .. GENERATED FROM PYTHON SOURCE LINES 451-454 .. code-block:: default from sklearn import metrics metrics.r2_score(y, full_data_predictor.predict(X_imputed)) .. rst-class:: sphx-glr-script-out .. code-block:: none 0.7011318399077224 .. GENERATED FROM PYTHON SOURCE LINES 455-458 This prediction is less good than on the full data, but this is expected, as missing values lead to a loss of information. We can compare it to a model trained to predict on data with missing values .. GENERATED FROM PYTHON SOURCE LINES 458-465 .. code-block:: default X_train, y_train = generate_mcar(n_samples, missing_rate=.5) na_predictor = HistGradientBoostingRegressor() na_predictor.fit(X_train, y_train) metrics.r2_score(y, na_predictor.predict(X)) .. rst-class:: sphx-glr-script-out .. code-block:: none 0.7036144866135492 .. GENERATED FROM PYTHON SOURCE LINES 466-469 Applying a model valid on the full data to imputed data work almost as well as a model trained for missing values. The small loss in performance is because the imputation is imperfect. .. GENERATED FROM PYTHON SOURCE LINES 471-476 When the data-generation is non linear --------------------------------------- We now modify a bit the example above to consider the situation where y is a non-linear function of X .. GENERATED FROM PYTHON SOURCE LINES 476-488 .. code-block:: default X, y = generate_mcar(n_samples, missing_rate=.5) y = y ** 2 # Train a predictive model that works on fully-observed data: X_full, y_full = generate_without_missing_values(n_samples) y_full = y_full ** 2 full_data_predictor = HistGradientBoostingRegressor() full_data_predictor.fit(X_full, y_full) model_selection.cross_val_score(full_data_predictor, X_full, y_full) .. rst-class:: sphx-glr-script-out .. code-block:: none array([0.97018219, 0.96754963, 0.96600898, 0.96971664, 0.96795887]) .. GENERATED FROM PYTHON SOURCE LINES 489-492 Once again, we have a near-perfect predictor on fully-observed data On data with missing values: .. GENERATED FROM PYTHON SOURCE LINES 492-499 .. code-block:: default iterative_imputer = impute.IterativeImputer() X_imputed = iterative_imputer.fit_transform(X) from sklearn import metrics metrics.r2_score(y, full_data_predictor.predict(X_imputed)) .. rst-class:: sphx-glr-script-out .. code-block:: none 0.5330009632809711 .. GENERATED FROM PYTHON SOURCE LINES 500-503 The full-data predictor works much less well Now we use a model trained to predict on data with missing values .. GENERATED FROM PYTHON SOURCE LINES 503-511 .. code-block:: default X_train, y_train = generate_mcar(n_samples, missing_rate=.5) y_train = y_train ** 2 na_predictor = HistGradientBoostingRegressor() na_predictor.fit(X_train, y_train) metrics.r2_score(y, na_predictor.predict(X)) .. rst-class:: sphx-glr-script-out .. code-block:: none 0.657124508956336 .. GENERATED FROM PYTHON SOURCE LINES 512-526 The model trained on data with missing values works significantly better than that was optimal for the fully-observed data. **Only for linear mechanism is the model on full data also optimal for perfectly imputed data**. When the function linking X to y has curvature, this curvature turns uncertainty resulting from missingness into bias [#]_. .. [#] The detailed mathematical analysis of prediction after imputation can be found here: https://arxiv.org/abs/2106.00311 | ________ .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 10.502 seconds) .. _sphx_glr_download_gen_notes_01_missing_values.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/dirty-data-science/python/gh-pages?filepath=notes/gen_notes/01_missing_values.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../lite/retro/notebooks/?path=gen_notes/01_missing_values.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: 01_missing_values.py <01_missing_values.py>` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: 01_missing_values.ipynb <01_missing_values.ipynb>` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_