# π Solution for Exercise M1.04ΒΆ

The goal of this exercise is to evaluate the impact of using an arbitrary integer encoding for categorical variables along with a linear classification model such as Logistic Regression.

To do so, letβs try to use `OrdinalEncoder`

to preprocess the categorical
variables. This preprocessor is assembled in a pipeline with
`LogisticRegression`

. The generalization performance of the pipeline can be
evaluated by cross-validation and then compared to the score obtained when
using `OneHotEncoder`

or to some other baseline score.

First, we load the dataset.

```
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"])
```

In the previous notebook, we used `sklearn.compose.make_column_selector`

to
automatically select columns with a specific data type (also called `dtype`

).
Here, we will use this selector to get only the columns containing strings
(column with `object`

dtype) that correspond to categorical features in our
dataset.

```
from sklearn.compose import make_column_selector as selector
categorical_columns_selector = selector(dtype_include=object)
categorical_columns = categorical_columns_selector(data)
data_categorical = data[categorical_columns]
```

Define a scikit-learn pipeline composed of an `OrdinalEncoder`

and a
`LogisticRegression`

classifier.

Because `OrdinalEncoder`

can raise errors if it sees an unknown category at
prediction time, you can set the `handle_unknown="use_encoded_value"`

and
`unknown_value`

parameters. You can refer to the
scikit-learn documentation
for more details regarding these parameters.

```
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import OrdinalEncoder
from sklearn.linear_model import LogisticRegression
# solution
model = make_pipeline(
OrdinalEncoder(handle_unknown="use_encoded_value", unknown_value=-1),
LogisticRegression(max_iter=500))
```

Your model is now defined. Evaluate it using a cross-validation using
`sklearn.model_selection.cross_validate`

.

```
from sklearn.model_selection import cross_validate
# solution
cv_results = cross_validate(model, data_categorical, 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: 0.755 +/- 0.002
```

Using an arbitrary mapping from string labels to integers as done here causes the linear model to make bad assumptions on the relative ordering of categories.

This prevents the model from learning anything predictive enough and the cross-validated score is even lower than the baseline we obtained by ignoring the input data and just constantly predicting the most frequent class:

```
from sklearn.dummy import DummyClassifier
cv_results = cross_validate(DummyClassifier(strategy="most_frequent"),
data_categorical, 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: 0.761 +/- 0.000
```

Now, we would like to compare the generalization performance of our previous
model with a new model where instead of using an `OrdinalEncoder`

, we will
use a `OneHotEncoder`

. Repeat the model evaluation using cross-validation.
Compare the score of both models and conclude on the impact of choosing a
specific encoding strategy when using a linear model.

```
from sklearn.preprocessing import OneHotEncoder
# solution
model = make_pipeline(
OneHotEncoder(handle_unknown="ignore"),
LogisticRegression(max_iter=500))
cv_results = cross_validate(model, data_categorical, 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: 0.833 +/- 0.002
```

With the linear classifier chosen, using an encoding that does not assume any ordering lead to much better result.

The important message here is: linear model and `OrdinalEncoder`

are used
together only for ordinal categorical features, features with a specific
ordering. Otherwise, your model will perform poorly.