def main():
print("-- Gradient Boosting Regression --")
X, y = datasets.make_regression(n_features=1,
n_samples=150,
bias=0,
noise=5)
X_train, X_test, y_train, y_test = train_test_split(standardize(X),
y,
test_size=0.5)
clf = GradientBoostingRegressor(debug=True)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
print("Mean Squared Error:", mse)
# Plot the results
plt.scatter(X_test[:, 0], y_test, color='black')
plt.scatter(X_test[:, 0], y_pred, color='green')
plt.title("Gradient Boosting Regression (%.2f MSE)" % mse)
plt.show()
def main():
print("-- Classification Tree --")
data = datasets.load_iris()
X = data.data
y = data.target
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4)
clf = ClassificationTree()
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
pca = PCA()
pca.plot_in_2d(X_test,
y_pred,
title="Decision Tree",
accuracy=accuracy,
legend_labels=data.target_names)
print("-- Regression Tree --")
X, y = datasets.make_regression(n_features=1,
n_samples=100,
bias=0,
noise=5)
X_train, X_test, y_train, y_test = train_test_split(standardize(X),
y,
test_size=0.3)
clf = RegressionTree()
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
print("Mean Squared Error:", mse)
# Plot the results
plt.scatter(X_test[:, 0], y_test, color='black')
plt.scatter(X_test[:, 0], y_pred, color='green')
plt.title("Regression Tree (%.2f MSE)" % mse)
plt.show()
def main():
print("-- Gradient Boosting Classification --")
data = datasets.load_iris()
X = data.data
y = data.target
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4)
clf = GradientBoostingClassifier(debug=True)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
Plot().plot_in_2d(X_test,
y_pred,
title="Gradient Boosting",
accuracy=accuracy,
legend_labels=data.target_names)
print("-- Gradient Boosting Regression --")
X, y = datasets.make_regression(n_features=1,
n_samples=150,
bias=0,
noise=5)
X_train, X_test, y_train, y_test = train_test_split(standardize(X),
y,
test_size=0.5)
clf = GradientBoostingRegressor(debug=True)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
print("Mean Squared Error:", mse)
# Plot the results
plt.scatter(X_test[:, 0], y_test, color='black')
plt.scatter(X_test[:, 0], y_pred, color='green')
plt.title("Gradient Boosting Regression (%.2f MSE)" % mse)
plt.show()
def main():
print ("-- Classification Tree --")
data = datasets.load_iris()
X = data.data
y = data.target
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4)
clf = ClassificationTree()
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
accuracy = accuracy_score(y_test, y_pred)
print ("Accuracy:", accuracy)
Plot().plot_in_2d(X_test, y_pred,
title="Decision Tree",
accuracy=accuracy,
legend_labels=data.target_names)
print ("-- Regression Tree --")
X, y = datasets.make_regression(n_features=1, n_samples=100, bias=0, noise=5)
X_train, X_test, y_train, y_test = train_test_split(standardize(X), y, test_size=0.3)
clf = RegressionTree()
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
print ("Mean Squared Error:", mse)
# Plot the results
plt.scatter(X_test[:, 0], y_test, color='black')
plt.scatter(X_test[:, 0], y_pred, color='green')
plt.title("Regression Tree (%.2f MSE)" % mse)
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():
print("-- Regression Tree --")
# 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 = 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)
clf = RegressionTree()
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
# 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"].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 = 11
# 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:
clf = PolynomialRidgeRegression(degree=poly_degree,
reg_factor=reg_factor,
learning_rate=0.001,
n_iterations=10000)
clf.fit(_X_train, _y_train)
y_pred = clf.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
clf = PolynomialRidgeRegression(degree=poly_degree,
reg_factor=best_reg_factor,
learning_rate=0.001,
n_iterations=10000)
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 (given by reg. factor: %s)" % (lowest_error, best_reg_factor))
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():
# 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 # 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)
n_samples, n_features = np.shape(X)
# Prior parameters
# - Weights are assumed distr. according to a Normal distribution
# - The variance of the weights are assumed distributed according to
# a scaled inverse chi-squared distribution.
# High prior uncertainty!
# Normal
mu0 = np.array([0] * n_features)
omega0 = np.diag([.0001] * n_features)
# Scaled inverse chi-squared
nu0 = 1
sigma_sq0 = 100
# The credible interval
cred_int = 10
clf = BayesianRegression(n_draws=2000,
poly_degree=4,
mu0=mu0,
omega0=omega0,
nu0=nu0,
sigma_sq0=sigma_sq0,
cred_int=cred_int)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
# Get prediction line
y_pred_, y_lower_, y_upper_ = clf.predict(X=X, eti=True)
# Print the mean squared error
print("Mean Squared Error:", mse)
# 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)
p1 = plt.plot(366 * X,
y_pred_,
color="black",
linewidth=2,
label="Prediction")
p2 = plt.plot(366 * X,
y_lower_,
color="gray",
linewidth=2,
label="{0}% Credible Interval".format(cred_int))
p3 = plt.plot(366 * X, y_upper_, color="gray", linewidth=2)
plt.axis((0, 366, -20, 25))
plt.suptitle("Bayesian Regression")
plt.title("MSE: %.2f" % mse, fontsize=10)
plt.xlabel('Day')
plt.ylabel('Temperature in Celcius')
plt.legend(loc='lower right')
# plt.legend((m1, m2), ("Training data", "Test data"), loc='lower right')
plt.legend(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 = np.atleast_2d(data["temp"].values).T
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)
n_samples, n_features = np.shape(X)
# Prior parameters
# - Weights are assumed distr. according to a Normal distribution
# - The variance of the weights are assumed distributed according to
# a scaled inverse chi-squared distribution.
# High prior uncertainty!
# Normal
mu0 = np.array([0] * n_features)
omega0 = np.diag([.0001] * n_features)
# Scaled inverse chi-squared
nu0 = 1
sigma_sq0 = 100
# The credible interval
cred_int = 10
clf = BayesianRegression(n_draws=2000,
poly_degree=4,
mu0=mu0,
omega0=omega0,
nu0=nu0,
sigma_sq0=sigma_sq0,
cred_int=cred_int)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
# Get prediction line
y_pred_, y_lower_, y_upper_ = clf.predict(X=X, eti=True)
# Print the mean squared error
print ("Mean Squared Error:", mse)
# 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)
p1 = plt.plot(366 * X, y_pred_, color="black", linewidth=2, label="Prediction")
p2 = plt.plot(366 * X, y_lower_, color="gray", linewidth=2, label="{0}% Credible Interval".format(cred_int))
p3 = plt.plot(366 * X, y_upper_, color="gray", linewidth=2)
plt.axis((0, 366, -20, 25))
plt.suptitle("Bayesian Regression")
plt.title("MSE: %.2f" % mse, fontsize=10)
plt.xlabel('Day')
plt.ylabel('Temperature in Celcius')
plt.legend(loc='lower right')
# plt.legend((m1, m2), ("Training data", "Test data"), loc='lower right')
plt.legend(loc='lower right')
plt.show()
