Ill-conditioned matrix warning

Module 4. Linear Models Regularization in linear model
#1

While going through the regularization lecture, I encountered this error repeated several times:

from sklearn.linear_model import Ridge

ridge = make_pipeline(PolynomialFeatures(degree=2),
                      Ridge(alpha=100))

cv_results = cross_validate(ridge, 
                            data, target,
                            cv=10, 
                            scoring="neg_mean_squared_error",
                            return_train_score=True,
                            return_estimator=True)

/opt/conda/lib/python3.9/site-packages/sklearn/linear_model/_ridge.py:147: LinAlgWarning: Ill-conditioned matrix (rcond=2.672e-17): result may not be accurate.
  return linalg.solve(A, Xy, sym_pos=True,
/opt/conda/lib/python3.9/site-packages/sklearn/linear_model/_ridge.py:147: LinAlgWarning: Ill-conditioned matrix (rcond=2.67257e-17): result may not be accurate.
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What is the issue here?

#2

Indeed, you should continue the notebook and get some intuitions. In short, it is due to not scaling the data that make the matrix X after feature expansion ill-conditioned. You will see that scaling the data within the pipeline will solve that issue.