def cv_analysis(x,
y,
z,
degrees,
k,
regression=linear_regression.OLS_SVD,
lambd=None):
scaler = StandardScaler()
MSE_test = np.empty(degrees.size)
for i, deg in enumerate(degrees):
X = linear_regression.design_matrix(x, y, deg)
# Normalize the design matrix
X = scaler.fit_transform(X)
X[:, 0] = np.ones(X.shape[0])
if regression != "LASSO":
MSE_test[i] = cross_validation.cross_validation(
X, z, k_folds=k, regression=regression)
else:
MSE_test[i] = cross_validation.cross_validation_lasso(X,
z,
k_folds=k,
lambd=lambd)
return MSE_test
def OLS_unit_test(min_deg=0, max_deg=15, tol=1e-6):
n = 100 # Number of data points
# Prepare data set
x = np.random.uniform(0, 1, n)
y = np.random.uniform(0, 1, n)
z = FrankeFunction(x, y) + np.random.normal(0, 1, n) * 0.2
degrees = np.arange(min_deg, max_deg + 1)
for deg in degrees:
# Set up design matrix
X = linear_regression.design_matrix(x, y, 5)
# Compute optimal parameters using our homegrown OLS
beta = linear_regression.OLS(X=X, z=z)
# Compute optimal parameters using sklearn
skl_reg = LinearRegression(fit_intercept=False).fit(X, z)
beta_skl = skl_reg.coef_
for i in range(len(beta)):
if abs(beta[i] - beta_skl[i]) < tol:
pass
else:
print("Warning! mismatch with SKL in OLS_unit_test with tol = %.0e" % tol)
print("Parameter no. %i for deg = %i" % (i, deg))
print("-> (OUR) beta = %8.12f" % beta[i])
print("-> (SKL) beta = %8.12f" % beta_skl[i])
return
def bootstrap_analysis(x,
y,
z,
degrees,
N_bootstraps,
regression=linear_regression.OLS_SVD,
lambd=None):
scaler = StandardScaler()
MSE_test = np.empty(degrees.size)
bias2_test = np.empty(degrees.size)
variance_test = np.empty(degrees.size)
for i, deg in enumerate(degrees):
X = linear_regression.design_matrix(x, y, deg)
# Split data, but don't shuffle. OK since data is already randomly sampled!
# Facilitates a direct comparison of the clean & Noisy data
X_train, X_test, z_train, z_test = train_test_split(X,
z,
test_size=0.2,
shuffle=False)
# Normalize data sets
X_train = scaler.fit_transform(X_train)
X_train[:, 0] = np.ones(X_train.shape[0])
X_test = scaler.fit_transform(X_test)
X_test[:, 0] = np.ones(X_test.shape[0])
# Lasso requires special treatment due to difference between SKL's way of doing things
# And our codes
if regression != "LASSO":
MSE_test[i], bias2_test[i], variance_test[i] = bootstrap.bootstrap(
X_train,
X_test,
z_train,
z_test,
bootstraps=N_bootstraps,
regression=regression)
else:
MSE_test[i], bias2_test[i], variance_test[
i] = bootstrap.bootstrap_lasso(X_train,
X_test,
z_train,
z_test,
bootstraps=N_bootstraps,
lambd=lambd)
return MSE_test, bias2_test, variance_test