# π 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
ames_housing = pd.read_csv("../datasets/ames_housing_no_missing.csv")
target_name = "SalePrice"
data = ames_housing.drop(columns=target_name)
target = ames_housing[target_name]
```

`ames_housing`

is a pandas dataframe. The column βSalePriceβ 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)

*Select a single answer*

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 βlast positionβ.

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

*Select a single answer*

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"`

*Select a single answer*

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

*Select all answers that apply*

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 βGarageAreaβ feature reduces the noise in the dataset

c) Just some random effects

*Select a single answer*

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

*Select a single answer*

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

*Select a single answer*

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

*Select a single answer*

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

*Select a single answer*