def test_mc_poly_verification(self):
dim = 1
alpha = np.array([[0, 1, 2]])
par = np.array([[1.0, 1]])
model = BayesSardModel(1,
par,
multi_ind=2,
point_str='ut',
point_par=self.pt_par_ut)
px = model._exp_x_px(alpha)
xpx = model._exp_x_xpx(alpha)
pxpx = model._exp_x_pxpx(alpha)
kxpx = model._exp_x_kxpx(par, alpha, self.data_1d)
# approximate expectations using cumulative moving average MC
def cma_mc(new_samples, old_avg, old_avg_size, axis=0):
b_size = new_samples.shape[axis]
return (new_samples.sum(axis=axis) +
old_avg_size * old_avg) / (old_avg_size + b_size)
batch_size = 100000
num_iter = 100
px_mc, xpx_mc, pxpx_mc, kxpx_mc = 0, 0, 0, 0
for i in range(num_iter):
# sample from standard Gaussian
x_samples = np.random.multivariate_normal(np.zeros((dim, )),
np.eye(dim),
size=batch_size).T
p = vandermonde(alpha, x_samples) # (N, Q)
k = model.kernel.eval(par, x_samples, self.data_1d,
scaling=False) # (N, M)
px_mc = cma_mc(p, px_mc, i * batch_size, axis=0)
xpx_mc = cma_mc(x_samples[..., na] * p[na, ...],
xpx_mc,
i * batch_size,
axis=1)
pxpx_mc = cma_mc(p[:, na, :] * p[..., na],
pxpx_mc,
i * batch_size,
axis=0)
kxpx_mc = cma_mc(k[..., na] * p[:, na, :],
kxpx_mc,
i * batch_size,
axis=0)
# compare MC approximates with analytic expressions
tol = 5e-3
print('Maximum absolute difference using {:d} samples.'.format(
batch_size * num_iter))
print('px {:.2e}'.format(np.abs(px - px_mc).max()))
print('xpx {:.2e}'.format(np.abs(xpx - xpx_mc).max()))
print('pxpx {:.2e}'.format(np.abs(pxpx - pxpx_mc).max()))
print('kxpx {:.2e}'.format(np.abs(kxpx - kxpx_mc).max()))
self.assertLessEqual(np.abs(px - px_mc).max(), tol)
self.assertLessEqual(np.abs(xpx - xpx_mc).max(), tol)
self.assertLessEqual(np.abs(pxpx - pxpx_mc).max(), tol)
self.assertLessEqual(np.abs(kxpx - kxpx_mc).max(), tol)
def test_exp_x_kxpx(self):
model = BayesSardModel(1,
self.ker_par_1d,
multi_ind=2,
point_str='ut',
point_par=self.pt_par_ut)
mi_1d = np.array([[0, 1, 2]])
par_1d = np.array([[1.0, 1.0]])
data = np.array([[0, 1, -1]], dtype=np.float)
ke = model._exp_x_kxpx(par_1d, mi_1d, data)
ke_true = np.array([[2**(-0.5), 0, 1 / (2 * (2**0.5))],
[
2**(-0.5) * np.exp(-0.25),
np.exp(-0.25) / (2 * (2**0.5)),
3 * np.exp(-0.25) / (4 * 2**0.5)
],
[
2**(-0.5) * np.exp(-0.25),
-np.exp(-0.25) / (2 * (2**0.5)),
3 * np.exp(-0.25) / (4 * 2**0.5)
]])
self.assertTrue(ke.shape == (data.shape[1], mi_1d.shape[1]))
self.assertTrue(np.allclose(ke, ke_true))