1. Python Machine learning - Regularized Linear Model

Linear Regression

from sklearn.linear_model import LinearRegression     

lin_reg = LinearRegression()

lin_reg.fit(X, y)

print(lin_reg.intercept_, lin_reg.coef_)

lin_reg.predict(X_new)

Polynomial Regression

Transform to polynomial feature

from sklearn.preprocessing import PolynomialFeatures

poly_features = PolynomialFeatures(degree =2, include_bias=False)

X_poly = poly_features.fit_transform(X) --- X_poly will have two terms - degree =1 and degree 2

Now use Linear Regression

lin_reg = LinearRegression()

lin_reg.fit(X_poly, y)

print(lin_reg.intercept_, lin_reg.coef_)

Training and test error

from sklearn.metrics import mean_squared_error

from sklearn.model_selection import train_test_split

def plot_learning_curves(model, x, y):

      X_train, X_val, Y_train, y_val = train_test_split(x, y, test_size=0.2)

      train_error, val_errors = [], []

      for m in range(1, len(X_train)):

             model.fit(X_train[:m], y_train[:m])

             y_train_predict = model.predict(X_train[:m])  -- no of sampling of training is changing from 1 to len(X_train)

             y_val_predict = model.predict(X_val) -- always taken for all validation samples.

              train_errors.append(mean_squared_error(y_train[:m], y_val_predict[:m]))

              val_errors.append(mean_squared_error(y_val, y_val_predict))

plt.plot(np.sqrt(train_errors, "r-+", linewidth=2, label="train"))

plt.plot(np.sqrt(val_errors, "b-+", linewidth=2, label="validation"))           

Using Pipeline

from   sklearn.pipeline import Pipeline

polynomial_regression = Pipeline ([

                                           ("poly features", PolynomialFeatures(degree=10, include_bias=False)),

                                           ("lin reg", LinearRegression())

                                            ])

plot_learning_curve(polynomial_regression, X, y)

Gradient Regression

Batch Gradient Descent

Stochastic Gradient Descent

Mini Batch Gradient Descent

Ridge Regression

from sklearn.linear_model import Ridge

ridge_reg = Ridge(alpha=1, solver="cholesky")

ridge_reg.fit(X,y)

ridge_reg.predict([1.5])

Lasso Regression ( Lest Absolute Shrinkage and Selection Operator Regression )

from sklearn.linear_model import Lasso

lasso_reg = Lasso(alpha = 0.1)

lasso_reg.fit(X, y)

lasso_reg.predict([1.5])

Elastic net

from sklearn.linear_model import ElasticNet

elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5)

elastic_net.fit(X,y)

elastic_net.predict([1.5])