Regularized regression

Supervised Learning with scikit-learn

George Boorman

Core Curriculum Manager, DataCamp

Why regularize?

Recall: Linear regression minimizes a loss function
It chooses a coefficient, $a$, for each feature variable, plus $b$
Large coefficients can lead to overfitting
Regularization: Penalize large coefficients

Ridge regression

Loss function = OLS loss function + $$ \alpha * \sum_{i=1}^{n} {a_i}^2$$
Ridge penalizes large positive or negative coefficients
$\alpha$: parameter we need to choose
Picking $\alpha$ is similar to picking k in KNN
Hyperparameter: variable used to optimize model parameters
$\alpha$ controls model complexity
- $\alpha$ = 0 = OLS (Can lead to overfitting)
- Very high $\alpha$: Can lead to underfitting

Ridge regression in scikit-learn

from sklearn.linear_model import Ridge

scores = []
for alpha in [0.1, 1.0, 10.0, 100.0, 1000.0]:

    ridge = Ridge(alpha=alpha)

    ridge.fit(X_train, y_train)
    y_pred = ridge.predict(X_test)

    scores.append(ridge.score(X_test, y_test))

print(scores)

[0.2828466623222221, 0.28320633574804777, 0.2853000732200006, 
 0.26423984812668133, 0.19292424694100963]

Lasso regression

Loss function = OLS loss function + $$ \alpha * \sum_{i=1}^{n} |a_i|$$

Lasso regression in scikit-learn

from sklearn.linear_model import Lasso

scores = []
for alpha in [0.01, 1.0, 10.0, 20.0, 50.0]:
  lasso = Lasso(alpha=alpha)
  lasso.fit(X_train, y_train)
  lasso_pred = lasso.predict(X_test)
  scores.append(lasso.score(X_test, y_test))
print(scores)

[0.99991649071123, 0.99961700284223, 0.93882227671069, 0.74855318676232, -0.05741034640016]

Lasso regression for feature selection

Lasso can select important features of a dataset
Shrinks the coefficients of less important features to zero
Features not shrunk to zero are selected by lasso

Lasso for feature selection in scikit-learn

from sklearn.linear_model import Lasso

X = diabetes_df.drop("glucose", axis=1).values
y = diabetes_df["glucose"].values
names = diabetes_df.drop("glucose", axis=1).columns

lasso = Lasso(alpha=0.1)

lasso_coef = lasso.fit(X, y).coef_

plt.bar(names, lasso_coef)
plt.xticks(rotation=45)
plt.show()

Lasso for feature selection in scikit-learn

bar plot of coefficients for each feature, with all around zero except for diabetes with a value of 25

Let's practice!

Supervised Learning with scikit-learn