# 4.4. Imputation of missing values¶

For various reasons, many real world datasets contain missing values, often encoded as blanks, NaNs or other placeholders. Such datasets however are incompatible with scikit-learn estimators which assume that all values in an array are numerical, and that all have and hold meaning. A basic strategy to use incomplete datasets is to discard entire rows and/or columns containing missing values. However, this comes at the price of losing data which may be valuable (even though incomplete). A better strategy is to impute the missing values, i.e., to infer them from the known part of the data. See the Glossary of Common Terms and API Elements entry on imputation.

The SimpleImputer class provides basic strategies for imputing missing values. Missing values can be imputed with a provided constant value, or using the statistics (mean, median or most frequent) of each column in which the missing values are located. This class also allows for different missing values encodings.

The following snippet demonstrates how to replace missing values, encoded as np.nan, using the mean value of the columns (axis 0) that contain the missing values:

>>> import numpy as np
>>> from sklearn.impute import SimpleImputer
>>> imp = SimpleImputer(missing_values=np.nan, strategy='mean')
>>> imp.fit([[1, 2], [np.nan, 3], [7, 6]])
SimpleImputer(copy=True, fill_value=None, missing_values=nan, strategy='mean', verbose=0)
>>> X = [[np.nan, 2], [6, np.nan], [7, 6]]
>>> print(imp.transform(X))
[[4.          2.        ]
[6.          3.666...]
[7.          6.        ]]


The SimpleImputer class also supports sparse matrices:

>>> import scipy.sparse as sp
>>> X = sp.csc_matrix([[1, 2], [0, -1], [8, 4]])
>>> imp = SimpleImputer(missing_values=-1, strategy='mean')
>>> imp.fit(X)
SimpleImputer(copy=True, fill_value=None, missing_values=-1, strategy='mean', verbose=0)
>>> X_test = sp.csc_matrix([[-1, 2], [6, -1], [7, 6]])
>>> print(imp.transform(X_test).toarray())
[[3. 2.]
[6. 3.]
[7. 6.]]


Note that this format is not meant to be used to implicitly store missing values in the matrix because it would densify it at transform time. Missing values encoded by 0 must be used with dense input.

The SimpleImputer class also supports categorical data represented as string values or pandas categoricals when using the 'most_frequent' or 'constant' strategy:

>>> import pandas as pd
>>> df = pd.DataFrame([["a", "x"],
...                    [np.nan, "y"],
...                    ["a", np.nan],
...                    ["b", "y"]], dtype="category")
...
>>> imp = SimpleImputer(strategy="most_frequent")
>>> print(imp.fit_transform(df))
[['a' 'x']
['a' 'y']
['a' 'y']
['b' 'y']]


SimpleImputer can be used in a Pipeline as a way to build a composite estimator that supports imputation. See Imputing missing values before building an estimator.

## 4.4.1. Marking imputed values¶

The MissingIndicator transformer is useful to transform a dataset into corresponding binary matrix indicating the presence of missing values in the dataset. This transformation is useful in conjunction with imputation. When using imputation, preserving the information about which values had been missing can be informative.

NaN is usually used as the placeholder for missing values. However, it enforces the data type to be float. The parameter missing_values allows to specify other placeholder such as integer. In the following example, we will use -1 as missing values:

>>> from sklearn.impute import MissingIndicator
>>> X = np.array([[-1, -1, 1, 3],
...               [4, -1, 0, -1],
...               [8, -1, 1, 0]])
>>> indicator = MissingIndicator(missing_values=-1)
array([[ True,  True, False],
[False,  True,  True],
[False,  True, False]])


The features parameter is used to choose the features for which the mask is constructed. By default, it is 'missing-only' which returns the imputer mask of the features containing missing values at fit time:

>>> indicator.features_
array([0, 1, 3])


The features parameter can be set to 'all' to returned all features whether or not they contain missing values:

>>> indicator = MissingIndicator(missing_values=-1, features="all")
array([[ True,  True, False, False],
[False,  True, False,  True],
[False,  True, False, False]])
>>> indicator.features_
array([0, 1, 2, 3])


When using the MissingIndicator in a Pipeline, be sure to use the FeatureUnion or ColumnTransformer to add the indicator features to the regular features. First we obtain the iris dataset, and add some missing values to it.

>>> from sklearn.datasets import load_iris
>>> from sklearn.impute import SimpleImputer, MissingIndicator
>>> from sklearn.model_selection import train_test_split
>>> from sklearn.pipeline import FeatureUnion, make_pipeline
>>> from sklearn.tree import DecisionTreeClassifier
>>> mask = np.random.randint(0, 2, size=X.shape).astype(np.bool)
>>> X_train, X_test, y_train, _ = train_test_split(X, y, test_size=100,
...                                                random_state=0)


Now we create a FeatureUnion. All features will be imputed using SimpleImputer, in order to enable classifiers to work with this data. Additionally, it adds the the indicator variables from MissingIndicator.

>>> transformer = FeatureUnion(
...     transformer_list=[
...         ('features', SimpleImputer(strategy='mean')),
...         ('indicators', MissingIndicator())])
>>> transformer = transformer.fit(X_train, y_train)
>>> results = transformer.transform(X_test)
>>> results.shape
(100, 8)


Of course, we cannot use the transformer to make any predictions. We should wrap this in a Pipeline with a classifier (e.g., a DecisionTreeClassifier) to be able to make predictions.

>>> clf = make_pipeline(transformer, DecisionTreeClassifier())
>>> clf = clf.fit(X_train, y_train)
>>> results = clf.predict(X_test)
>>> results.shape
(100,)