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 = 13 model = ElasticNet(degree=15, reg_factor=0.01, l1_ratio=0.7, learning_rate=0.001, n_iterations=4000) model.fit(X_train, y_train) # Training error plot n = len(model.training_errors) training, = plt.plot(range(n), model.training_errors, label="Training Error") plt.legend(handles=[training]) plt.title("Error Plot") plt.ylabel('Mean Squared Error') plt.xlabel('Iterations') plt.show() 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, 0.05)) 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("Elastic Net") 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()
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 = 13 model = ElasticNet(degree=15, reg_factor=0.01, l1_ratio=0.7, learning_rate=0.001, n_iterations=4000) model.fit(X_train, y_train) # Training error plot n = len(model.training_errors) training, = plt.plot(range(n), model.training_errors, label="Training Error") plt.legend(handles=[training]) plt.title("Error Plot") plt.ylabel('Mean Squared Error') plt.xlabel('Iterations') plt.show() 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, 0.05)) 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("Elastic Net") 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()
def main(): X, y = make_regression(n_samples=100, n_features=1, noise=20) X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4) n_samples, n_features = np.shape(X) model = LinearRegression(n_iterations=100) model.fit(X_train, y_train) # Training error plot n = len(model.training_errors) training, = plt.plot(range(n), model.training_errors, label="Training Error") plt.legend(handles=[training]) plt.title("Error Plot") plt.ylabel('Mean Squared Error') plt.xlabel('Iterations') plt.show() y_pred = model.predict(X_test) mse = mean_squared_error(y_test, y_pred) print("Mean squared error: %s" % (mse)) 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("Linear 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()
def main(): X, y = make_regression(n_samples=1000, n_features=1, noise=10) X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4) model = LassoRegression(degree=15, reg_factor=0.05, learning_rate=0.001, n_iterations=4000) model.fit(X_train, y_train) n = len(model.training_errors) training, = plt.plot(range(n), model.training_errors, label='Training Error') plt.legend(handles=[training]) plt.title('Error Plot') plt.ylabel('Mean Squared Error') plt.xlabel('Iterations') plt.show() y_pred = model.predict(X_test) mse = mean_squared_error(y_test, y_pred) print('Mean Squared Error: {} (given by reg_factor : {}'.format(mse, 0.5)) y_pred_line = model.predict(X) 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("Lasso Regression") plt.title("MSE: {}".format(mse, fontsize=10)) plt.xlabel('X') plt.ylabel('Y') plt.legend((m1, m2), ("Training data", "Test data"), loc='lower right') plt.show()
def main(): # Load temperature data data = pd.read_csv('mlfromscratch/data/TempLinkoping2016.txt', sep="\t") time = np.atleast_2d(data["time"].as_matrix()).T temp = np.atleast_2d(data["temp"].as_matrix()).T X = time # Time. Fraction of the year [0, 1] y = temp[:, 0] # Temperature. Reduce to one-dim X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4) n_samples, n_features = np.shape(X) clf = LinearRegression() clf.fit(X_train, y_train) y_pred = clf.predict(X_test) mse = mean_squared_error(y_test, y_pred) print("Mean squared error: %s" % (mse)) y_pred_line = clf.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()
def main(): X, y = make_regression(n_samples=100, n_features=1, noise=20) X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4) n_samples, n_features = np.shape(X) model = LinearRegression(n_iterations=100) model.fit(X_train, y_train) # Training error plot n = len(model.training_errors) training, = plt.plot(range(n), model.training_errors, label="Training Error") plt.legend(handles=[training]) plt.title("Error Plot") plt.ylabel('Mean Squared Error') plt.xlabel('Iterations') plt.show() y_pred = model.predict(X_test) mse = mean_squared_error(y_test, y_pred) print ("Mean squared error: %s" % (mse)) 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("Linear 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()
def main(): print("-- Regression Tree --") # Load temperature data data = pd.read_csv('mlfromscratch/data/TempLinkoping2016.txt', sep="\t") time = np.atleast_2d(data["time"].values).T temp = np.atleast_2d(data["temp"].values).T X = standardize(time) # Time. Fraction of the year [0, 1] y = temp[:, 0] # Temperature. Reduce to one-dim X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3) model = RegressionTree() model.fit(X_train, y_train) y_pred = model.predict(X_test) y_pred_line = model.predict(X) # Color map cmap = plt.get_cmap('viridis') mse = mean_squared_error(y_test, y_pred) print("Mean Squared Error:", mse) # Plot the results # 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) m3 = plt.scatter(366 * X_test, y_pred, color='black', s=10) plt.suptitle("Regression Tree") plt.title("MSE: %.2f" % mse, fontsize=10) plt.xlabel('Day') plt.ylabel('Temperature in Celcius') plt.legend((m1, m2, m3), ("Training data", "Test data", "Prediction"), loc='lower right') plt.show()
def main(): print("-- Gradient Boosting Regression --") # Load temperature data data = pd.read_csv('mlfromscratch/data/TempLinkoping2016.txt', sep="\t") time = np.atleast_2d(data["time"].as_matrix()).T temp = np.atleast_2d(data["temp"].as_matrix()).T X = time.reshape((-1, 1)) # Time. Fraction of the year [0, 1] X = np.insert(X, 0, values=1, axis=1) # Insert bias term y = temp[:, 0] # Temperature. Reduce to one-dim X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5) clf = GradientBoostingRegressor(debug=True) clf.fit(X_train, y_train) y_pred = clf.predict(X_test) y_pred_line = clf.predict(X) # Color map cmap = plt.get_cmap('viridis') mse = mean_squared_error(y_test, y_pred) print("Mean Squared Error:", mse) # Plot the results m1 = plt.scatter(366 * X_train[:, 1], y_train, color=cmap(0.9), s=10) m2 = plt.scatter(366 * X_test[:, 1], y_test, color=cmap(0.5), s=10) m3 = plt.scatter(366 * X_test[:, 1], y_pred, color='black', s=10) plt.suptitle("Regression Tree") plt.title("MSE: %.2f" % mse, fontsize=10) plt.xlabel('Day') plt.ylabel('Temperature in Celcius') plt.legend((m1, m2, m3), ("Training data", "Test data", "Prediction"), loc='lower right') plt.show()
def main(): print ("-- Regression Tree --") # Load temperature data data = pd.read_csv('mlfromscratch/data/TempLinkoping2016.txt', sep="\t") time = np.atleast_2d(data["time"].values).T temp = np.atleast_2d(data["temp"].values).T X = standardize(time) # Time. Fraction of the year [0, 1] y = temp[:, 0] # Temperature. Reduce to one-dim X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3) model = RegressionTree() model.fit(X_train, y_train) y_pred = model.predict(X_test) y_pred_line = model.predict(X) # Color map cmap = plt.get_cmap('viridis') mse = mean_squared_error(y_test, y_pred) print ("Mean Squared Error:", mse) # Plot the results # 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) m3 = plt.scatter(366 * X_test, y_pred, color='black', s=10) plt.suptitle("Regression Tree") plt.title("MSE: %.2f" % mse, fontsize=10) plt.xlabel('Day') plt.ylabel('Temperature in Celcius') plt.legend((m1, m2, m3), ("Training data", "Test data", "Prediction"), loc='lower right') plt.show()
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 = 0 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=best_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, best_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()
time_X = np.atleast_2d(data["day"].values).T temp = data["temperature"].values X = time_X # fraction of the year [0, 1] y = temp X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4, random_state=10) # Since the data is shuffled by train_test_split, we sort the test data to plot it neatly y_test = y_test[X_test.flatten().argsort()] X_test = np.sort(X_test, axis=0) poly = PolynomialFeatures(degree=5, include_bias=False) poly_X_train = poly.fit_transform(X_train) poly_X_test = poly.fit_transform(X_test) model = LinearRegression() model.fit(poly_X_train, y_train) y_pred = model.predict(poly_X_test) mse = mean_squared_error(y_pred, y_test) print("Mean Squared Error: ", mse) plt.scatter(X_train, y_train, c='g', s=20) plt.scatter(X_test, y_test, c='b', s=20) plt.plot(X_test, y_pred, linewidth=2, c='r') plt.legend() plt.show()
def main(): # Load temperature data data = pd.read_csv('mlfromscratch/data/TempLinkoping2016.txt', sep="\t") time = np.atleast_2d(data["time"].as_matrix()).T temp = data["temp"].as_matrix() 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=best_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)" % (lowest_error, best_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()