In [ ]:
%matplotlib inline

Imputing missing values with variants of IterativeImputer

.. currentmodule:: sklearn

The :class:~impute.IterativeImputer class is very flexible - it can be used with a variety of estimators to do round-robin regression, treating every variable as an output in turn.

In this example we compare some estimators for the purpose of missing feature imputation with :class:~impute.IterativeImputer:

  • :class:~linear_model.BayesianRidge: regularized linear regression
  • :class:~tree.DecisionTreeRegressor: non-linear regression
  • :class:~ensemble.ExtraTreesRegressor: similar to missForest in R
  • :class:~neighbors.KNeighborsRegressor: comparable to other KNN imputation approaches

Of particular interest is the ability of :class:~impute.IterativeImputer to mimic the behavior of missForest, a popular imputation package for R. In this example, we have chosen to use :class:~ensemble.ExtraTreesRegressor instead of :class:~ensemble.RandomForestRegressor (as in missForest) due to its increased speed.

Note that :class:~neighbors.KNeighborsRegressor is different from KNN imputation, which learns from samples with missing values by using a distance metric that accounts for missing values, rather than imputing them.

The goal is to compare different estimators to see which one is best for the :class:~impute.IterativeImputer when using a :class:~linear_model.BayesianRidge estimator on the California housing dataset with a single value randomly removed from each row.

For this particular pattern of missing values we see that :class:~ensemble.ExtraTreesRegressor and :class:~linear_model.BayesianRidge give the best results.

In [ ]:

import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

# To use this experimental feature, we need to explicitly ask for it:
from sklearn.experimental import enable_iterative_imputer  # noqa
from sklearn.datasets import fetch_california_housing
from sklearn.impute import SimpleImputer
from sklearn.impute import IterativeImputer
from sklearn.linear_model import BayesianRidge
from sklearn.tree import DecisionTreeRegressor
from sklearn.ensemble import ExtraTreesRegressor
from sklearn.neighbors import KNeighborsRegressor
from sklearn.pipeline import make_pipeline
from sklearn.model_selection import cross_val_score


rng = np.random.RandomState(0)

X_full, y_full = fetch_california_housing(return_X_y=True)
# ~2k samples is enough for the purpose of the example.
# Remove the following two lines for a slower run with different error bars.
X_full = X_full[::10]
y_full = y_full[::10]
n_samples, n_features = X_full.shape

# Estimate the score on the entire dataset, with no missing values
br_estimator = BayesianRidge()
score_full_data = pd.DataFrame(
        br_estimator, X_full, y_full, scoring='neg_mean_squared_error',
    columns=['Full Data']

# Add a single missing value to each row
X_missing = X_full.copy()
y_missing = y_full
missing_samples = np.arange(n_samples)
missing_features = rng.choice(n_features, n_samples, replace=True)
X_missing[missing_samples, missing_features] = np.nan

# Estimate the score after imputation (mean and median strategies)
score_simple_imputer = pd.DataFrame()
for strategy in ('mean', 'median'):
    estimator = make_pipeline(
        SimpleImputer(missing_values=np.nan, strategy=strategy),
    score_simple_imputer[strategy] = cross_val_score(
        estimator, X_missing, y_missing, scoring='neg_mean_squared_error',

# Estimate the score after iterative imputation of the missing values
# with different estimators
estimators = [
    DecisionTreeRegressor(max_features='sqrt', random_state=0),
    ExtraTreesRegressor(n_estimators=10, random_state=0),
score_iterative_imputer = pd.DataFrame()
for impute_estimator in estimators:
    estimator = make_pipeline(
        IterativeImputer(random_state=0, estimator=impute_estimator),
    score_iterative_imputer[impute_estimator.__class__.__name__] = \
            estimator, X_missing, y_missing, scoring='neg_mean_squared_error',

scores = pd.concat(
    [score_full_data, score_simple_imputer, score_iterative_imputer],
    keys=['Original', 'SimpleImputer', 'IterativeImputer'], axis=1

# plot california housing results
fig, ax = plt.subplots(figsize=(13, 6))
means = -scores.mean()
errors = scores.std()
means.plot.barh(xerr=errors, ax=ax)
ax.set_title('California Housing Regression with Different Imputation Methods')
ax.set_xlabel('MSE (smaller is better)')
ax.set_yticklabels([" w/ ".join(label) for label in means.index.tolist()])