def Kfold(x, y, z, folds, degree, lambd=None):
Xtrain, ztrain, Xtest, ztest = Evaluation.CV_split(x, y, z, folds)
MSE_alltrain = np.zeros(folds)
MSE_alltest = np.zeros(folds)
for i in range(folds):
# picking out the ith fold of training data
xtrain = Xtrain[i]
x = xtrain[:, 0]
y = xtrain[:, 1]
z = ztrain[i]
# Finding error for train data
X_train = Regression.CreateDesignMatrix_X(x, y, degree)
beta_train = Regression.Beta(X_train, z, lambd)
ztilde_train = Regression.Prediction(X_train, beta_train)
MSE_alltrain[i] = Evaluation.MSE(z, ztilde_train)
# picking out the ith fold for test data
xtest = Xtest[i]
x = xtest[:, 0]
y = xtest[:, 1]
z = ztest[i]
# Finding error for test data
X_test = Regression.CreateDesignMatrix_X(x, y, degree)
ztilde_test = Regression.Prediction(X_test, beta_train)
MSE_alltest[i] = Evaluation.MSE(ztest[i], ztilde_test)
MSEtrain = np.mean(MSE_alltrain)
MSEtest = np.mean(MSE_alltest)
return MSEtrain, MSEtest
def BiasVarTradeOff(x, y, z, folds, degree, lambd=None):
if len(x.shape) > 1 or len(y.shape) > 1 or len(z.shape) > 1:
x, y, z = x.flatten(), y.flatten(), z.flatten()
X = np.transpose(np.array([x, y, z]))
np.random.shuffle(X)
z = X[:, 2]
X = X[:, 0:2]
x_train, x_test, z_train, z_test = train_test_split(
X, z, test_size=0.2) # Make test data that is not used in Kfold CV
x1 = x_train[:, 0]
y1 = x_train[:, 1]
z1 = z_train
folds = folds - 1 ### obs needs to be done to do splitting. Means Kfold is done with k-1 folds!!!!
error_alltest = np.zeros(degree)
bias_alltest = np.zeros(degree)
var_alltest = np.zeros(degree)
for d in range(degree):
Xtrain, ztrain, Xtest, ztest = Evaluation.CV_split(
x1, y1, z1, folds)
ztilde_test = np.zeros([len(z_test), folds])
for i in range(folds):
xtrain = Xtrain[i]
x = xtrain[:, 0]
y = xtrain[:, 1]
X_train = Regression.CreateDesignMatrix_X(x, y, d)
beta_train = Regression.Beta(X_train, ztrain[i], lambd)
x = x_test[:, 0]
y = x_test[:, 1]
X_test = Regression.CreateDesignMatrix_X(x, y, d)
ztilde_test[:, i] = Regression.Prediction(X_test, beta_train)
z_test = z_test.reshape(z_test.shape[0], 1)
error_alltest[d] = np.mean(
np.mean((ztilde_test - z_test)**2, axis=1, keepdims=True))
bias_alltest[d] = np.mean(
(z_test - np.mean(ztilde_test, axis=1, keepdims=True))**2)
var_alltest[d] = np.mean(np.var(ztilde_test, axis=1,
keepdims=True))
return bias_alltest, var_alltest, error_alltest
