# π Exercise M4.03#

Now, we tackle a more realistic classification problem instead of making a
synthetic dataset. We start by loading the Adult Census dataset with the
following snippet. For the moment we retain only the **numerical features**.

```
import pandas as pd
adult_census = pd.read_csv("../datasets/adult-census.csv")
target = adult_census["class"]
data = adult_census.select_dtypes(["integer", "floating"])
data = data.drop(columns=["education-num"])
data
```

age | capital-gain | capital-loss | hours-per-week | |
---|---|---|---|---|

0 | 25 | 0 | 0 | 40 |

1 | 38 | 0 | 0 | 50 |

2 | 28 | 0 | 0 | 40 |

3 | 44 | 7688 | 0 | 40 |

4 | 18 | 0 | 0 | 30 |

... | ... | ... | ... | ... |

48837 | 27 | 0 | 0 | 38 |

48838 | 40 | 0 | 0 | 40 |

48839 | 58 | 0 | 0 | 40 |

48840 | 22 | 0 | 0 | 20 |

48841 | 52 | 15024 | 0 | 40 |

48842 rows Γ 4 columns

We confirm that all the selected features are numerical.

Compute the generalization performance in terms of accuracy of a linear model
composed of a `StandardScaler`

and a `LogisticRegression`

. Use a 10-fold
cross-validation with `return_estimator=True`

to be able to inspect the
trained estimators.

```
# Write your code here.
```

What is the most important feature seen by the logistic regression?

You can use a boxplot to compare the absolute values of the coefficients while also visualizing the variability induced by the cross-validation resampling.

```
# Write your code here.
```

Letβs now work with **both numerical and categorical features**. You can
reload the Adult Census dataset with the following snippet:

```
adult_census = pd.read_csv("../datasets/adult-census.csv")
target = adult_census["class"]
data = adult_census.drop(columns=["class", "education-num"])
```

Create a predictive model where:

The numerical data must be scaled.

The categorical data must be one-hot encoded, set

`min_frequency=0.01`

to group categories concerning less than 1% of the total samples.The predictor is a

`LogisticRegression`

. You may need to increase the number of`max_iter`

, which is 100 by default.

Use the same 10-fold cross-validation strategy with `return_estimator=True`

as
above to evaluate this complex pipeline.

```
# Write your code here.
```

By comparing the cross-validation test scores of both models fold-to-fold, count the number of times the model using both numerical and categorical features has a better test score than the model using only numerical features.

```
# Write your code here.
```

For the following questions, you can copy and paste the following snippet to
get the feature names from the column transformer here named `preprocessor`

.

```
preprocessor.fit(data)
feature_names = (
preprocessor.named_transformers_["onehotencoder"].get_feature_names_out(
categorical_columns
)
).tolist()
feature_names += numerical_columns
feature_names
```

```
# Write your code here.
```

Notice that there are as many feature names as coefficients in the last step of your predictive pipeline.

Which of the following pairs of features is most impacting the predictions of the logistic regression classifier based on the absolute magnitude of its coefficients?

```
# Write your code here.
```

Now create a similar pipeline consisting of the same preprocessor as above,
followed by a `PolynomialFeatures`

and a logistic regression with `C=0.01`

.
Set `degree=2`

and `interaction_only=True`

to the feature engineering step.
Remember not to include a βbiasβ feature to avoid introducing a redundancy
with the intercept of the subsequent logistic regression.

```
# Write your code here.
```

By comparing the cross-validation test scores of both models fold-to-fold, count the number of times the model using multiplicative interactions and both numerical and categorical features has a better test score than the model without interactions.

```
# Write your code here.
```

```
# Write your code here.
```