def test_predict_and_score(eng): X = randn(10, 2) y = fromarray(randn(10, 4).T, engine=eng) model = LinearRegression().fit(X, y) yhat = model.predict(X).toarray() rsq = model.score(X, y).toarray() truth = hstack([yhat, rsq[:, newaxis]]) result = model.predict_and_score(X, y).toarray() assert allclose(truth, result)
def test_predict_and_score(eng):
X = randn(10, 2)
y = fromarray(randn(10, 4).T, engine=eng)
model = LinearRegression().fit(X, y)
yhat = model.predict(X).toarray()
rsq = model.score(X, y).toarray()
truth = hstack([yhat, rsq[:, newaxis]])
result = model.predict_and_score(X, y).toarray()
assert allclose(truth, result)
def __test_cross_validation_methods():
# A small implementation of a test case
from regression import LinearRegression
import matplotlib.pyplot as plt
# Initial values
n = 100
N_bs = 1000
k_splits = 4
test_percent = 0.2
noise = 0.3
np.random.seed(1234)
# Sets up random matrices
x = np.random.rand(n, 1)
def func_excact(_x): return 2*_x*_x + np.exp(-2*_x) + noise * \
np.random.randn(_x.shape[0], _x.shape[1])
y = func_excact(x)
def design_matrix(_x):
return np.c_[np.ones(_x.shape), _x, _x * _x]
# Sets up design matrix
X = design_matrix(x)
# Performs regression
reg = LinearRegression()
reg.fit(X, y)
y = y.ravel()
y_predict = reg.predict(X).ravel()
print("Regular linear regression")
print("R2: {:-20.16f}".format(reg.score(y, y_predict)))
print("MSE: {:-20.16f}".format(metrics.mse(y, y_predict)))
# print (metrics.bias(y, y_predict))
print("Bias^2:{:-20.16f}".format(metrics.bias2(y, y_predict)))
# Small plotter
import matplotlib.pyplot as plt
plt.plot(x, y, "o", label="data")
plt.plot(x,
y_predict,
"o",
label=r"Pred, $R^2={:.4f}$".format(reg.score(y, y_predict)))
print("k-fold Cross Validation")
kfcv = kFoldCrossValidation(x, y, LinearRegression, design_matrix)
kfcv.cross_validate(k_splits=k_fold_size, test_percent=test_percent)
print("R2: {:-20.16f}".format(kfcv.R2))
print("MSE: {:-20.16f}".format(kfcv.MSE))
print("Bias^2:{:-20.16f}".format(kfcv.bias))
print("Var(y):{:-20.16f}".format(kfcv.var))
print("MSE = Bias^2 + Var(y) = ")
print("{} = {} + {} = {}".format(kfcv.MSE, kfcv.bias, kfcv.var,
kfcv.bias + kfcv.var))
print("Diff: {}".format(abs(kfcv.bias + kfcv.var - kfcv.MSE)))
plt.errorbar(kfcv.x_pred_test,
kfcv.y_pred,
yerr=np.sqrt(kfcv.y_pred_var),
fmt="o",
label=r"k-fold CV, $R^2={:.4f}$".format(kfcv.R2))
print("kk Cross Validation")
kkcv = kkFoldCrossValidation(x, y, LinearRegression, design_matrix)
kkcv.cross_validate(k_splits=k_fold_size, test_percent=test_percent)
print("R2: {:-20.16f}".format(kkcv.R2))
print("MSE: {:-20.16f}".format(kkcv.MSE))
print("Bias^2:{:-20.16f}".format(kkcv.bias))
print("Var(y):{:-20.16f}".format(kkcv.var))
print("MSE = Bias^2 + Var(y) = ")
print("{} = {} + {} = {}".format(kkcv.MSE, kkcv.bias, kkcv.var,
kkcv.bias + kkcv.var))
print("Diff: {}".format(abs(kkcv.bias + kkcv.var - kkcv.MSE)))
plt.errorbar(kkcv.x_pred_test.ravel(),
kkcv.y_pred.ravel(),
yerr=np.sqrt(kkcv.y_pred_var.ravel()),
fmt="o",
label=r"kk-fold CV, $R^2={:.4f}$".format(kkcv.R2))
print("Monte Carlo Cross Validation")
mccv = MCCrossValidation(x, y, LinearRegression, design_matrix)
mccv.cross_validate(N_bs, k_splits=k_fold_size, test_percent=test_percent)
print("R2: {:-20.16f}".format(mccv.R2))
print("MSE: {:-20.16f}".format(mccv.MSE))
print("Bias^2:{:-20.16f}".format(mccv.bias))
print("Var(y):{:-20.16f}".format(mccv.var))
print("MSE = Bias^2 + Var(y) = ")
print("{} = {} + {} = {}".format(mccv.MSE, mccv.bias, mccv.var,
mccv.bias + mccv.var))
print("Diff: {}".format(abs(mccv.bias + mccv.var - mccv.MSE)))
print("\nCross Validation methods tested.")
plt.errorbar(mccv.x_pred_test,
mccv.y_pred,
yerr=np.sqrt(mccv.y_pred_var),
fmt="o",
label=r"MC CV, $R^2={:.4f}$".format(mccv.R2))
plt.xlabel(r"$x$")
plt.ylabel(r"$y$")
plt.title(r"$y=2x^2$")
plt.legend()
plt.show()
def __test_bootstrap_fit():
# A small implementation of a test case
from regression import LinearRegression
N_bs = 1000
# Initial values
n = 200
noise = 0.2
np.random.seed(1234)
test_percent = 0.35
# Sets up random matrices
x = np.random.rand(n, 1)
def func_excact(_x): return 2*_x*_x + np.exp(-2*_x) + noise * \
np.random.randn(_x.shape[0], _x.shape[1])
y = func_excact(x)
def design_matrix(_x):
return np.c_[np.ones(_x.shape), _x, _x*_x]
# Sets up design matrix
X = design_matrix(x)
# Performs regression
reg = LinearRegression()
reg.fit(X, y)
y = y.ravel()
y_predict = reg.predict(X).ravel()
print("Regular linear regression")
print("R2: {:-20.16f}".format(reg.score(y_predict, y)))
print("MSE: {:-20.16f}".format(metrics.mse(y, y_predict)))
print("Beta: ", reg.coef_.ravel())
print("var(Beta): ", reg.coef_var.ravel())
print("")
# Performs a bootstrap
print("Bootstrapping")
bs_reg = BootstrapRegression(x, y, LinearRegression, design_matrix)
bs_reg.bootstrap(N_bs, test_percent=test_percent)
print("R2: {:-20.16f}".format(bs_reg.R2))
print("MSE: {:-20.16f}".format(bs_reg.MSE))
print("Bias^2:{:-20.16f}".format(bs_reg.bias))
print("Var(y):{:-20.16f}".format(bs_reg.var))
print("Beta: ", bs_reg.coef_.ravel())
print("var(Beta): ", bs_reg.coef_var.ravel())
print("MSE = Bias^2 + Var(y) = ")
print("{} = {} + {} = {}".format(bs_reg.MSE, bs_reg.bias, bs_reg.var,
bs_reg.bias + bs_reg.var))
print("Diff: {}".format(abs(bs_reg.bias + bs_reg.var - bs_reg.MSE)))
import matplotlib.pyplot as plt
plt.plot(x.ravel(), y, "o", label="Data")
plt.plot(x.ravel(), y_predict, "o",
label=r"Pred, R^2={:.4f}".format(reg.score(y_predict, y)))
print (bs_reg.y_pred.shape, bs_reg.y_pred_var.shape)
plt.errorbar(bs_reg.x_pred_test, bs_reg.y_pred,
yerr=np.sqrt(bs_reg.y_pred_var), fmt="o",
label=r"Bootstrap Prediction, $R^2={:.4f}$".format(bs_reg.R2))
plt.xlabel(r"$x$")
plt.ylabel(r"$y$")
plt.title(r"$2x^2 + \sigma^2$")
plt.legend()
plt.show()