📝 Exercise M4.03

📝 Exercise M4.03#

Now, we tackle a (relatively) 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 × 4 columns

We confirm that all the selected features are numerical.

Define a linear model composed of a StandardScaler followed by a LogisticRegression with default parameters.

Then use a 10-fold cross-validation to estimate its generalization performance in terms of accuracy. Also set 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.

Let’s 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 with default parameters, except that 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 the full pipeline, including the feature scaling and encoding preprocessing.

# 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 and enough max_iter. Set degree=2 and interaction_only=True to the feature engineering step. Remember not to include a “bias” feature to avoid introducing a redundancy with the intercept of the subsequent logistic regression.

# Write your code here.

Use the same 10-fold cross-validation strategy as above to evaluate this pipeline with interactions. In this case there is no need to return the estimator, as the number of features generated by the PolynomialFeatures step is much too large to be able to visually explore the learned coefficients of the final classifier.

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.