code: def main():
      # Load temperature data
      data = pd.read_csv(
          "mlfromscratch/data/TempLinkoping2016.txt", sep="\t"
      )
  
      time = np.atleast_2d(data["time"].values).T
      temp = data["temp"].values
  
      X = time  # fraction of the year [0, 1]
      y = temp
  
      X_train, X_test, y_train, y_test = train_test_split(
          X, y, test_size=0.4
      )
  
      poly_degree = 15
  
      # Finding regularization constant using cross validation
      lowest_error = float("inf")
      best_reg_factor = None
      print("Finding regularization constant using cross validation:")
      k = 10
      for reg_factor in np.arange(0, 0.1, 0.01):
          cross_validation_sets = k_fold_cross_validation_sets(
              X_train, y_train, k=k
          )
          mse = 0
          for (
              _X_train,
              _X_test,
              _y_train,
              _y_test,
          ) in cross_validation_sets:
              model = PolynomialRidgeRegression(
                  degree=poly_degree,
                  reg_factor=reg_factor,
                  learning_rate=0.001,
                  n_iterations=10000,
              )
              model.fit(_X_train, _y_train)
              y_pred = model.predict(_X_test)
              _mse = mean_squared_error(_y_test, y_pred)
              mse += _mse
          mse /= k
  
          # Print the mean squared error
          print(
              "\tMean Squared Error: %s (regularization: %s)"
              % (mse, reg_factor)
          )
  
          # Save reg. constant that gave lowest error
          if mse < lowest_error:
              best_reg_factor = reg_factor
              lowest_error = mse
  
      # Make final prediction
      model = PolynomialRidgeRegression(
          degree=poly_degree,
          reg_factor=reg_factor,
          learning_rate=0.001,
          n_iterations=10000,
      )
      model.fit(X_train, y_train)
  
      y_pred = model.predict(X_test)
      mse = mean_squared_error(y_test, y_pred)
      print(
          "Mean squared error: %s (given by reg. factor: %s)"
          % (mse, reg_factor)
      )
  
      y_pred_line = model.predict(X)
  
      # Color map
      cmap = plt.get_cmap("viridis")
  
      # Plot the results
      m1 = plt.scatter(366 * X_train, y_train, color=cmap(0.9), s=10)
      m2 = plt.scatter(366 * X_test, y_test, color=cmap(0.5), s=10)
      plt.plot(
          366 * X,
          y_pred_line,
          color="black",
          linewidth=2,
          label="Prediction",
      )
      plt.suptitle("Polynomial Ridge Regression")
      plt.title("MSE: %.2f" % mse, fontsize=10)
      plt.xlabel("Day")
      plt.ylabel("Temperature in Celcius")
      plt.legend(
          (m1, m2), ("Training data", "Test data"), loc="lower right"
      )
      plt.show()
  
file_path: ML-From-Scratch/mlfromscratch/examples/ridge_regression.py
imports: from __future__ import print_function
  import matplotlib.pyplot
  import numpy
  import pandas
  from mlfromscratch.supervised_learning import PolynomialRidgeRegression
  from mlfromscratch.utils import k_fold_cross_validation_sets, normalize, Plot
  from mlfromscratch.utils import train_test_split, polynomial_features, mean_squared_error
label_desc: Use image node_id 1 for calling a global function with example usage: main() without return types