def OSLRegression(x, y, z, degree=5, l=0.1):
# Split into training and test
x_train = np.random.rand(100, 1)
y_train = np.random.rand(100, 1)
z = FrankeFunction(x_train, y_train)
# traning data and finding design matrix X_
X = np.c_[x_train, y_train]
poly = PolynomialFeatures(degree)
X_ = poly.fit_transform(X)
clf = linear_model.LassoCV()
clf.fit(X_, z)
print("X_: ", np.shape(X_))
beta = clf.coef_
# predicting and preparing plot
x_, y_ = np.meshgrid(x, y)
x = x_.reshape(-1, 1)
y = y_.reshape(-1, 1)
M = np.c_[x, y]
M_ = poly.fit_transform(M)
predict = M_.dot(beta.T)
# plotting
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(x_,
y_,
predict.reshape(20, 20),
cmap=cm.coolwarm,
linewidth=0,
antialiased=False)
plt.show()
return beta
def LassoRegression(x, y, z, degree=5, alpha=10**(-7), verbose=False):
# Split into training and test
x_train = np.random.rand(100, 1)
y_train = np.random.rand(100, 1)
z = FrankeFunction(x_train, y_train)
# train and find design matrix X_
X = np.c_[x_train, y_train]
poly = PolynomialFeatures(degree)
X_ = poly.fit_transform(X)
clf = linear_model.Lasso(alpha, fit_intercept=False)
clf.fit(X_, z)
beta = clf.coef_
# predict
x_, y_ = np.meshgrid(x, y)
x = x_.reshape(-1, 1)
y = y_.reshape(-1, 1)
M = np.c_[x, y]
M_ = poly.fit_transform(M)
predict = M_.dot(beta.T)
if verbose:
print("x: ", np.shape(x))
print("y: ", np.shape(y))
print("M: ", np.shape(M))
print("M_: ", np.shape(M_))
print("predict: ", np.shape(predict))
design = np.dot(np.transpose(X), X)
# plot
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(x_,
y_,
predict.reshape(20, 20),
cmap=cm.coolwarm,
linewidth=0,
antialiased=False)
plt.show()
return beta, design
def RidgeRegression(x, y, z, degree=5, alpha=10**(-6), verbose=False):
# Split into training and test
x_train = np.random.rand(100, 1)
y_train = np.random.rand(100, 1)
z = FrankeFunction(x_train, y_train)
# training and finding design matrix X_
X = np.c_[x_train, y_train]
poly = PolynomialFeatures(degree)
X_ = poly.fit_transform(X)
ridge = linear_model.RidgeCV(alphas=np.array([alpha]))
ridge.fit(X_, z)
beta = ridge.coef_
#intercept = ridge.intercept_
# predict data and prepare for plotting
x_, y_ = np.meshgrid(x, y)
x = x_.reshape(-1, 1)
y = y_.reshape(-1, 1)
M = np.c_[x, y]
M_ = poly.fit_transform(M)
predict = M_.dot(beta.T)
if verbose:
print("X_: ", np.shape(X_))
print("M: ", np.shape(M))
print("M_: ", np.shape(M_))
print("predict: ", np.shape(predict))
# show figure
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(x_,
y_,
predict.reshape(20, 20),
cmap=cm.coolwarm,
linewidth=0,
antialiased=False)
plt.show()
return beta
from R2 import R2
from predict import predict
from bootstrap import bootstrap
from frankeFunction import FrankeFunction
#from OrdinaryLeastSquare import ols
#Read data
#terrain_over_Norway = imread('SRTM_data_Norway_1.tif')
#Choose to lo look at a little part of the data-set:
#terrain = terrain_over_Norway[0:100,0:100]
x = np.arange(0, 1, 0.05)
y = np.arange(0, 1, 0.05)
x, y = np.meshgrid(x, y)
n = np.size(x, 0)
terrain = FrankeFunction(x, y)
"""
#plot of the original
plt.figure()
plt.title('Terrain')
plt.imshow(terrain_over_Norway, cmap='gray')
plt.xlabel('X')
plt.ylabel('Y')
plt.savefig('oiginal_subset.png')
plt.show()
"""
num_rows = len(terrain)
num_cols = len(terrain[0])
num_observations = num_rows * num_cols
X = np.zeros((num_observations, 3))
design = np.dot(np.transpose(X), X)
# plot
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(x_,
y_,
predict.reshape(20, 20),
cmap=cm.coolwarm,
linewidth=0,
antialiased=False)
plt.show()
return beta, design
if __name__ == '__main__':
#terrain1 = misc.imread('data.tif',flatten=0)
verbose = True
x = np.arange(0, 1, 0.05).reshape((20, 1))
y = np.arange(0, 1, 0.05).reshape((20, 1))
z = FrankeFunction(x, y)
beta, design = LassoRegression(x, y, z, 5, alpha=10**(-7), verbose=True)
if verbose:
print("beta values: ", beta)
print("design: ", design)
beta_list = beta.ravel().tolist()
cofint = mean_confidence_interval(beta_list)
if verbose: print("mean_confidence_interval: ", cofint)