# π Solution for Exercise M1.05ΒΆ

The goal of this exercise is to evaluate the impact of feature preprocessing on a pipeline that uses a decision-tree-based classifier instead of logistic regression.

The first question is to empirically evaluate whether scaling numerical feature is helpful or not;

The second question is to evaluate whether it is empirically better (both from a computational and a statistical perspective) to use integer coded or one-hot encoded categories.

```
import pandas as pd
adult_census = pd.read_csv("../datasets/adult-census.csv")
```

```
target_name = "class"
target = adult_census[target_name]
data = adult_census.drop(columns=[target_name, "education-num"])
```

As in the previous notebooks, we use the utility `make_column_selector`

to only select column with a specific data type. Besides, we list in
advance all categories for the categorical columns.

```
from sklearn.compose import make_column_selector as selector
numerical_columns_selector = selector(dtype_exclude=object)
categorical_columns_selector = selector(dtype_include=object)
numerical_columns = numerical_columns_selector(data)
categorical_columns = categorical_columns_selector(data)
```

## Reference pipeline (no numerical scaling and integer-coded categories)ΒΆ

First letβs time the pipeline we used in the main notebook to serve as a reference:

```
%%time
from sklearn.model_selection import cross_validate
from sklearn.pipeline import make_pipeline
from sklearn.compose import ColumnTransformer
from sklearn.preprocessing import OrdinalEncoder
from sklearn.experimental import enable_hist_gradient_boosting
from sklearn.ensemble import HistGradientBoostingClassifier
categorical_preprocessor = OrdinalEncoder(handle_unknown="use_encoded_value",
unknown_value=-1)
preprocessor = ColumnTransformer([
('categorical', categorical_preprocessor, categorical_columns)],
remainder="passthrough")
model = make_pipeline(preprocessor, HistGradientBoostingClassifier())
cv_results = cross_validate(model, data, target)
scores = cv_results["test_score"]
print("The mean cross-validation accuracy is: "
f"{scores.mean():.3f} +/- {scores.std():.3f}")
```

```
The mean cross-validation accuracy is: 0.873 +/- 0.003
CPU times: user 6.49 s, sys: 84.9 ms, total: 6.58 s
Wall time: 6.58 s
```

## Scaling numerical featuresΒΆ

```
%%time
from sklearn.preprocessing import StandardScaler
preprocessor = ColumnTransformer([
('numerical', StandardScaler(), numerical_columns),
('categorical', OrdinalEncoder(handle_unknown="use_encoded_value",
unknown_value=-1),
categorical_columns)])
model = make_pipeline(preprocessor, HistGradientBoostingClassifier())
cv_results = cross_validate(model, data, target)
scores = cv_results["test_score"]
print("The mean cross-validation accuracy is: "
f"{scores.mean():.3f} +/- {scores.std():.3f}")
```

```
The mean cross-validation accuracy is: 0.873 +/- 0.003
CPU times: user 6.21 s, sys: 67.8 ms, total: 6.27 s
Wall time: 6.27 s
```

### AnalysisΒΆ

We can observe that both the accuracy and the training time are approximately the same as the reference pipeline (any time difference you might observe is not significant).

Scaling numerical features is indeed useless for most decision tree models in
general and for `HistGradientBoostingClassifier`

in particular.

## One-hot encoding of categorical variablesΒΆ

For linear models, we have observed that integer coding of categorical
variables can be very detrimental. However for
`HistGradientBoostingClassifier`

models, it does not seem to be the case as
the cross-validation of the reference pipeline with `OrdinalEncoder`

is good.

Letβs see if we can get an even better accuracy with `OneHotEncoder`

.

Hint: `HistGradientBoostingClassifier`

does not yet support sparse input
data. You might want to use
`OneHotEncoder(handle_unknown="ignore", sparse=False)`

to force the use of a
dense representation as a workaround.

```
%%time
from sklearn.preprocessing import OneHotEncoder
categorical_preprocessor = OneHotEncoder(handle_unknown="ignore", sparse=False)
preprocessor = ColumnTransformer([
('one-hot-encoder', categorical_preprocessor, categorical_columns)],
remainder="passthrough")
model = make_pipeline(preprocessor, HistGradientBoostingClassifier())
cv_results = cross_validate(model, data, target)
scores = cv_results["test_score"]
print("The mean cross-validation accuracy is: "
f"{scores.mean():.3f} +/- {scores.std():.3f}")
```

```
The mean cross-validation accuracy is: 0.874 +/- 0.002
CPU times: user 20.8 s, sys: 204 ms, total: 21 s
Wall time: 21 s
```

### AnalysisΒΆ

From an accuracy point of view, the result is almost exactly the same.
The reason is that `HistGradientBoostingClassifier`

is expressive
and robust enough to deal with misleading ordering of integer coded
categories (which was not the case for linear models).

However from a computation point of view, the training time is
significantly longer: this is caused by the fact that `OneHotEncoder`

generates approximately 10 times more features than `OrdinalEncoder`

.

Note that the current implementation `HistGradientBoostingClassifier`

is still incomplete, and once sparse representation are handled
correctly, training time might improve with such kinds of encodings.

The main take away message is that arbitrary integer coding of
categories is perfectly fine for `HistGradientBoostingClassifier`

and yields fast training times.