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# Imputing missing values with variants of IterativeImputer¶

The `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 `IterativeImputer`

:

`BayesianRidge`

: regularized linear regression`RandomForestRegressor`

: Forests of randomized trees regression`Nystroem`

,`Ridge`

): a pipeline with the expansion of a degree 2 polynomial kernel and regularized linear regression`KNeighborsRegressor`

: comparable to other KNN imputation approaches

Of particular interest is the ability of
`IterativeImputer`

to mimic the behavior of missForest, a
popular imputation package for R.

Note that `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
`IterativeImputer`

when using a
`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
`BayesianRidge`

and
`RandomForestRegressor`

give the best results.

It should be noted that some estimators such as
`HistGradientBoostingRegressor`

can natively deal with
missing features and are often recommended over building pipelines with
complex and costly missing values imputation strategies.

```
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, Ridge
from sklearn.kernel_approximation import Nystroem
from sklearn.ensemble import RandomForestRegressor
from sklearn.neighbors import KNeighborsRegressor
from sklearn.pipeline import make_pipeline
from sklearn.model_selection import cross_val_score
N_SPLITS = 5
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(
cross_val_score(
br_estimator, X_full, y_full, scoring="neg_mean_squared_error", cv=N_SPLITS
),
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), br_estimator
)
score_simple_imputer[strategy] = cross_val_score(
estimator, X_missing, y_missing, scoring="neg_mean_squared_error", cv=N_SPLITS
)
# Estimate the score after iterative imputation of the missing values
# with different estimators
estimators = [
BayesianRidge(),
RandomForestRegressor(
# We tuned the hyperparameters of the RandomForestRegressor to get a good
# enough predictive performance for a restricted execution time.
n_estimators=4,
max_depth=10,
bootstrap=True,
max_samples=0.5,
n_jobs=2,
random_state=0,
),
make_pipeline(
Nystroem(kernel="polynomial", degree=2, random_state=0), Ridge(alpha=1e3)
),
KNeighborsRegressor(n_neighbors=15),
]
score_iterative_imputer = pd.DataFrame()
# iterative imputer is sensible to the tolerance and
# dependent on the estimator used internally.
# we tuned the tolerance to keep this example run with limited computational
# resources while not changing the results too much compared to keeping the
# stricter default value for the tolerance parameter.
tolerances = (1e-3, 1e-1, 1e-1, 1e-2)
for impute_estimator, tol in zip(estimators, tolerances):
estimator = make_pipeline(
IterativeImputer(
random_state=0, estimator=impute_estimator, max_iter=25, tol=tol
),
br_estimator,
)
score_iterative_imputer[impute_estimator.__class__.__name__] = cross_val_score(
estimator, X_missing, y_missing, scoring="neg_mean_squared_error", cv=N_SPLITS
)
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_yticks(np.arange(means.shape[0]))
ax.set_yticklabels([" w/ ".join(label) for label in means.index.tolist()])
plt.tight_layout(pad=1)
plt.show()
```

**Total running time of the script:** ( 0 minutes 3.073 seconds)