# 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.

## 4.4.1. Univariate feature 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, 3], [7, 6]])
>>> imp = SimpleImputer(missing_values=0, strategy='mean')
>>> imp.fit(X)
SimpleImputer(copy=True, fill_value=None, missing_values=0, strategy='mean', verbose=0)
>>> X_test = sp.csc_matrix([[0, 2], [6, 0], [7, 6]])
>>> print(imp.transform(X_test))
[[4. 2. ]
[6. 3.666...]
[7. 6. ]]
```

Note that, here, missing values are encoded by 0 and are thus implicitly stored in the matrix. This format is thus suitable when there are many more missing values than observed values.

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']]
```

## 4.4.2. Multivariate feature imputation¶

A more sophisticated approach is to use the `MICEImputer`

class, which
implements the Multivariate Imputation by Chained Equations technique. MICE
models each feature with missing values as a function of other features, and
uses that estimate for imputation. It does so in a round-robin fashion: at
each step, a feature column is designated as output y and the other feature
columns are treated as inputs X. A regressor is fit on (X, y) for known y.
Then, the regressor is used to predict the unknown values of y. This is
repeated for each feature, and then is done for a number of imputation rounds.
Here is an example snippet:

```
>>> import numpy as np
>>> from sklearn.impute import MICEImputer
>>> imp = MICEImputer(n_imputations=10, random_state=0)
>>> imp.fit([[1, 2], [np.nan, 3], [7, np.nan]])
MICEImputer(imputation_order='ascending', initial_strategy='mean',
max_value=None, min_value=None, missing_values=nan, n_burn_in=10,
n_imputations=10, n_nearest_features=None, predictor=None,
random_state=0, verbose=False)
>>> X_test = [[np.nan, 2], [6, np.nan], [np.nan, 6]]
>>> print(np.round(imp.transform(X_test)))
[[ 1. 2.]
[ 6. 4.]
[13. 6.]]
```

Both `SimpleImputer`

and `MICEImputer`

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.