# 🏁 Wrap-up quiz 4#

This quiz requires some programming to be answered.

Open the dataset ames_housing_no_missing.csv with the following command:

import pandas as pd

target_name = "SalePrice"
data = ames_housing.drop(columns=target_name)
target = ames_housing[target_name]


ames_housing is a pandas dataframe. The column “SalePrice” contains the target variable.

To simplify this exercise, we will only used the numerical features defined below:

numerical_features = [
"LotFrontage", "LotArea", "MasVnrArea", "BsmtFinSF1", "BsmtFinSF2",
"BsmtUnfSF", "TotalBsmtSF", "1stFlrSF", "2ndFlrSF", "LowQualFinSF",
"GrLivArea", "BedroomAbvGr", "KitchenAbvGr", "TotRmsAbvGrd", "Fireplaces",
"GarageCars", "GarageArea", "WoodDeckSF", "OpenPorchSF", "EnclosedPorch",
"3SsnPorch", "ScreenPorch", "PoolArea", "MiscVal",
]

data_numerical = data[numerical_features]


Start by fitting a ridge regressor (sklearn.linear_model.Ridge) fixing the penalty alpha to 0 to not regularize the model. Use a 10-fold cross-validation and pass the argument return_estimator=True in sklearn.model_selection.cross_validate to access all fitted estimators fitted on each fold. As discussed in the previous notebooks, use an instance of sklearn.preprocessing.StandardScaler to scale the data before passing it to the regressor.

Question

How large is the largest absolute value of the weight (coefficient) in this trained model?

• a) Lower than 1.0 (1e0)

• b) Between 1.0 (1e0) and 100,000.0 (1e5)

• c) Larger than 100,000.0 (1e5)

Hint: Note that the estimator fitted in each fold of the cross-validation procedure is a pipeline object. To access the coefficients of the Ridge model at the last position in a pipeline object, you can use the expression pipeline[-1].coef_ for each pipeline object fitted in the cross-validation procedure. The -1 notation is a negative index meaning “last position”.

Repeat the same experiment by fitting a ridge regressor (sklearn.linear_model.Ridge) with the default parameter (i.e. alpha=1.0).

Question

How large is the largest absolute value of the weight (coefficient) in this trained model?

• a) Lower than 1.0

• b) Between 1.0 and 100,000.0

• c) Larger than 100,000.0

Question

What are the two most important features used by the ridge regressor? You can make a box-plot of the coefficients across all folds to get a good insight.

• a) "MiscVal" and "BsmtFinSF1"

• b) "GarageCars" and "GrLivArea"

• c) "TotalBsmtSF" and "GarageCars"

Remove the feature "GarageArea" from the dataset and repeat the previous experiment.

Question

What is the impact on the weights of removing "GarageArea" from the dataset?

• a) None

• b) Completely changes the order of the most important features

• c) Decreases the standard deviation (across CV folds) of the "GarageCars" coefficient

Question

What is the main reason for observing the previous impact on the most important weight(s)?

• a) Both garage features are correlated and are carrying similar information

• b) Removing the “GarageArea” feature reduces the noise in the dataset

• c) Just some random effects

Now, we will search for the regularization strength that maximizes the generalization performance of our predictive model. Fit a sklearn.linear_model.RidgeCV instead of a Ridge regressor on the numerical data without the "GarageArea" column. Pass alphas=np.logspace(-3, 3, num=101) to explore the effect of changing the regularization strength.

Question

What is the effect of tuning alpha on the variability of the weights of the feature "GarageCars"? Remember that the variability can be assessed by computing the standard deviation.

• a) The variability does not change after tuning alpha

• b) The variability decreased after tuning alpha

• c) The variability increased after tuning alpha

Check the parameter alpha_ (the regularization strength) for the different ridge regressors obtained on each fold.

Question

In which range does alpha_ fall into for most folds?

• a) between 0.1 and 1

• b) between 1 and 10

• c) between 10 and 100

• d) between 100 and 1000

So far we only used the list of numerical_features to build the predictive model. Now create a preprocessor to deal separately with the numerical and categorical columns:

• categorical features can be selected if they have an object data type;

• use an OneHotEncoder to encode the categorical features;

• numerical features should correspond to the numerical_features as defined above. This is a subset of the features that are not an object data type;

• use an StandardScaler to scale the numerical features.

The last step of the pipeline should be a RidgeCV with the same set of alphas to evaluate as previously.

Question

By comparing the cross-validation test scores fold-to-fold for the model with numerical_features only and the model with both numerical_features and categorical_features, count the number of times the simple model has a better test score than the model with all features. Select the range which this number belongs to:

• a) [0, 3]: the simple model is consistently worse than the model with all features

• b) [4, 6]: both models are almost equivalent

• c) [7, 10]: the simple model is consistently better than the model with all features

In this Module we saw that non-linear feature engineering may yield a more predictive pipeline, as long as we take care of adjusting the regularization to avoid overfitting.

Try this approach by building a new pipeline similar to the previous one but replacing the StandardScaler by a SplineTransformer (with default hyperparameter values) to better model the non-linear influence of the numerical features.

Furthermore, let the new pipeline model feature interactions by adding a new Nystroem step between the preprocessor and the RidgeCV estimator. Set kernel="poly", degree=2 and n_components=300 for this new feature engineering step.

Question

By comparing the cross-validation test scores fold-to-fold for the model with both numerical_features and categorical_features, and the model that performs non-linear feature engineering; count the number of times the non-linear pipeline has a better test score than the model with simpler preprocessing. Select the range which this number belongs to:

• a) [0, 3]: the new non-linear pipeline is consistently worse than the previous pipeline

• b) [4, 6]: both models are almost equivalent

• c) [7, 10]: the new non-linear pipeline is consistently better than the previous pipeline