def test_ridge_regression_with_penalty_is_less_than_without_penalty():
X = randn(2, 2)
Y = randn(2)
assert norm(utils.ridge_regression(X, Y, c1=2.0)[0]) <= norm(
utils.ridge_regression(X, Y)[0])
assert norm(utils.ridge_regression(X, Y, c1=1.0, c2=1.0)[0]) <= norm(
utils.ridge_regression(X, Y)[0])
def test_ridge_regression_with_extreme_c2_penalty_equals_close_to_offset():
c1 = 0.0
c2 = 10e8
offset = np.ones(2)
X = randn(2, 2)
Y = randn(2)
assert norm(utils.ridge_regression(X, Y, c1, c2, offset)[0] - offset) < 10e-4
def test_ridge_regression_with_extreme_c1_penalty_equals_close_to_zero_vector():
c1 = 10e8
c2 = 0.0
offset = np.ones(2)
X = randn(2, 2)
Y = randn(2)
assert norm(utils.ridge_regression(X, Y, c1, c2, offset)[0]) < 10e-4
def test_ridge_regression_with_extreme_c2_penalty_equals_close_to_offset():
c1 = 0.0
c2 = 10e8
offset = np.ones(2)
X = randn(2, 2)
Y = randn(2)
assert norm(utils.ridge_regression(X, Y, c1, c2, offset)[0] - offset) < 10e-4
def test_ridge_regression_with_extreme_c1_penalty_equals_close_to_zero_vector():
c1 = 10e8
c2 = 0.0
offset = np.ones(2)
X = randn(2, 2)
Y = randn(2)
assert norm(utils.ridge_regression(X, Y, c1, c2, offset)[0]) < 10e-4
def test_lstsq_returns_correct_values():
X = np.array([[-1.0, -1.0], [-1.0, 0], [-.8, -1.0],
[1.0, 1.0], [1.0, 0.0]])
y = [1, 1, 1, -1, -1]
beta,V = utils.ridge_regression(X, y)
expected_beta = [-0.98684211, -0.07894737]
expected_v = [[-0.03289474, -0.49342105, 0.06578947, 0.03289474, 0.49342105],
[-0.30263158, 0.46052632, -0.39473684, 0.30263158, -0.46052632]]
assert(norm(beta - expected_beta) < 10e-4)
for V_row, e_v_row in zip(V, expected_v):
assert(norm(V_row - e_v_row) < 1e-4)
def test_lstsq_returns_correct_values():
X = np.array([[-1.0, -1.0], [-1.0, 0], [-.8, -1.0],
[1.0, 1.0], [1.0, 0.0]])
y = [1, 1, 1, -1, -1]
beta,V = utils.ridge_regression(X, y)
expected_beta = [-0.98684211, -0.07894737]
expected_v = [[-0.03289474, -0.49342105, 0.06578947, 0.03289474, 0.49342105],
[-0.30263158, 0.46052632, -0.39473684, 0.30263158, -0.46052632]]
assert(norm(beta - expected_beta) < 10e-4)
for V_row, e_v_row in zip(V, expected_v):
assert(norm(V_row - e_v_row) < 1e-4)
def test_lstsq_returns_similar_values_to_ridge_regression():
X = randn(2, 2)
Y = randn(2)
expected = lstsq(X, Y, rcond=None)[0]
assert norm(utils.ridge_regression(X, Y)[0] - expected) < 10e-4
def test_lstsq_returns_similar_values_to_ridge_regression():
X = randn(2, 2)
Y = randn(2)
expected = lstsq(X, Y)[0]
assert norm(utils.ridge_regression(X, Y)[0] - expected) < 10e-4
def test_ridge_regression_with_penalty_is_less_than_without_penalty():
X = randn(2, 2)
Y = randn(2)
assert norm(utils.ridge_regression(X, Y, c1=2.0)[0]) <= norm(utils.ridge_regression(X, Y)[0])
assert norm(utils.ridge_regression(X, Y, c1=1.0, c2=1.0)[0]) <= norm(utils.ridge_regression(X, Y)[0])
def test_lstsq_returns_similar_values_to_ridge_regression():
offset = np.ones(2)
X = randn(2, 2)
Y = randn(2)
expected = lstsq(X, Y)[0]
assert norm(utils.ridge_regression(X, Y)[0] - expected) < 10e-4
