def test_mlgk_gradient(caseitem, nodal):
'''derivative w.r.t. hyperparameters'''
_, case = caseitem
G = case['graphs']
knode = case['knode']
kedge = case['kedge']
for q in case['q']:
mlgk = MarginalizedGraphKernel(knode, kedge, q=q)
np.set_printoptions(precision=4, linewidth=999, suppress=True)
R, dR = mlgk(G, nodal=nodal, eval_gradient=True)
assert (len(dR.shape) == 3)
assert (R.shape[0] == dR.shape[0])
assert (R.shape[1] == dR.shape[1])
assert (dR.shape[2] >= 1)
for i in range(len(mlgk.theta)):
theta = mlgk.theta
eps = 1e-3
t = np.copy(theta)
t[i] += eps
mlgk.theta = t
Rr = mlgk(G, nodal=nodal)
t = np.copy(theta)
t[i] -= eps
mlgk.theta = t
Rl = mlgk(G, nodal=nodal)
mlgk.theta = theta
dR_dLogt = (Rr - Rl) / (2 * eps)
dLogt_dt = 1 / np.exp(theta)[i]
dR_dt = dR_dLogt * dLogt_dt
assert np.allclose(dR[:, :, i], dR_dt, rtol=0.05, atol=0.05)
def test_mlgk_diag_gradient(caseitem, nodal):
'''derivative w.r.t. hyperparameters'''
_, case = caseitem
G = case['graphs']
knode = case['knode']
kedge = case['kedge']
for q in case['q']:
mlgk = MarginalizedGraphKernel(knode, kedge, q=q)
R, dR = mlgk.diag(G, nodal=nodal, eval_gradient=True)
assert (len(dR.shape) == 2)
assert (R.shape[0] == dR.shape[0])
assert (dR.shape[1] >= 1)
for i in range(len(mlgk.theta)):
theta = mlgk.theta
eps = 1e-3
t = np.copy(theta)
t[i] += eps
mlgk.theta = t
Rr = mlgk.diag(G, nodal=nodal, eval_gradient=False)
t = np.copy(theta)
t[i] -= eps
mlgk.theta = t
Rl = mlgk.diag(G, nodal=nodal, eval_gradient=False)
mlgk.theta = theta
dR_dLogt = (Rr - Rl) / (2 * eps)
dLogt_dt = 1 / np.exp(theta)[i]
dR_dt = dR_dLogt * dLogt_dt
for a, b in zip(dR[:, i].ravel(), dR_dt.ravel()):
assert (a == pytest.approx(b, rel=0.05, abs=0.05))