def test003(self):
p = 5
lmbda = 0.05
for _ in range(10):
R, X = self._create_case(p, T=1000)
B_hat, eps = solve_lasso(X, p=p, lmbda=lmbda,
maxiter=250, eps=-np.inf)
self.assertTrue(eps > 0)
J_star = exact_cost_function(B_hat, X, lmbda=lmbda)
for _ in range(10):
J = exact_cost_function(
B_hat + 0.025 * np.random.normal(size=B_hat.shape),
X, lmbda=lmbda)
self.assertTrue(J_star < J)
return
def test_exact_cost_function001(self):
X = np.array([[1.0, 2.0],
[-1.0, -2.0]])
B = np.array([[[2.2, 3.1],
[-1.8, 2.6]]])
cost_xp = (1. / 4) * (np.sum((X[1] - B[0] @ X[0])**2) +
np.sum(X[0]**2))
cost = exact_cost_function(B, X, lmbda=0.0, W=1.0)
self.assertAlmostEqual(cost, cost_xp)
return
def test_exact_cost_function002(self):
for _ in range(10):
X = np.random.normal(size=(3, 2))
B = np.array([[[2.2, 3.1],
[-1.8, 2.6]]])
cost_xp = (1. / 6) * (np.sum((X[2] - B[0] @ X[1])**2) +
np.sum((X[1] - B[0] @ X[0])**2) +
np.sum(X[0]**2))
cost = exact_cost_function(B, X, lmbda=0.0, W=1.0)
self.assertAlmostEqual(cost, cost_xp)
return
def test_exact_cost_function004(self):
for _ in range(10):
X = np.random.normal(size=(3, 2))
W = np.random.normal(size=(2, 2))
B = np.random.normal(size=(2, 2, 2))
cost_xp = ((1. / 6) * (
np.sum((X[2] - B[0] @ X[1] - B[1] @ X[0])**2) +
np.sum((X[1] - B[0] @ X[0])**2) +
np.sum(X[0]**2)) +
2 * np.sum(np.abs(W * B)))
cost = exact_cost_function(B, X, lmbda=2.0, W=W)
self.assertAlmostEqual(cost, cost_xp)
return