z = (z-z_mean)/np.sqrt(z_var)
k = 5 # number of folds
N_pol = [3, 5, 7] # polynomial degrees
lambdas = np.logspace(-4, 3, 8) # penalties
MSE_b = np.zeros([len(N_pol), len(lambdas)])
bias_b = np.zeros([len(N_pol), len(lambdas), 2])
var_b = np.zeros([len(N_pol), len(lambdas), 2])
MSE_k = np.zeros([len(N_pol), len(lambdas), 2])
for i, deg in enumerate(N_pol):
# prepare data
X = design_matrix(x, y, n=deg)
# preprocess data
scaler = StandardScaler()
scaler.fit(X)
X = scaler.transform(X)
for j, l in enumerate(lambdas):
# bootstrap
MSE_b[i,j], bias_b[i,j], var_b[i,j] = bias_variance_tradeoff(X, z,
500, model=Ridge, lambda_=l)
# kfold
MSE_k[i,j] = kfold(k, X, z, model=Ridge, lambda_=l)
for i, deg in enumerate(N_pol):
MSE_test = np.zeros(N)
MSE_train = np.zeros(N)
R2_test = np.zeros(N)
R2_train = np.zeros(N)
MSE_boots = np.zeros(N)
bias_boots = np.zeros([N, 2])
var_boots = np.zeros([N, 2])
MSE_kfold = np.zeros(N)
std_kfold = np.zeros(N)
for i in range(1, N+1):
# prepare data
X = design_matrix(x, y, n=i)
X_train, X_test, z_train, z_test = train_test_split(X, z, test_size=0.35)
# preprocess data
scaler_train = StandardScaler()
scaler_train.fit(X_train)
X_train = scaler_train.transform(X_train)
X_test = scaler_train.transform(X_test)
scaler_X = StandardScaler()
scaler_X.fit(X)
X = scaler_X.transform(X)
# fit
beta, beta_var = LinearRegression(X_train, z_train, r_var=1)