def test_rbm_fim(self):
j = np.random.normal(0, 1)
visbias = np.random.normal()
hidbias = np.random.normal()
model = IsingModel(2)
model.import_rbm01(1, 1, [visbias], [hidbias], [[j]])
z = (np.exp(visbias) + np.exp(hidbias) +
np.exp(visbias + hidbias + j) + 1)
def f(x):
return x / z * (1 - x / z)
exp0 = np.exp(visbias + hidbias + j)
exp1 = np.exp(visbias) + exp0
exp2 = np.exp(hidbias) + exp0
varvis = f(exp1)
varhid = f(exp2)
varprod = f(exp0)
cov_vishid = exp0 / z - exp1 * exp2 / z ** 2
cov_visprod = exp0 / z * (1 - exp1 / z)
cov_hidprod = exp0 / z * (1 - exp2 / z)
sample = model.sample(20000)
fim = model.fisher_information(sample, model.fimfunction_rbm)
self.assertAlmostEqual(fim[0, 0], varvis, places=2)
self.assertAlmostEqual(fim[1, 1], varhid, places=2)
self.assertAlmostEqual(fim[2, 2], varprod, places=2)
self.assertAlmostEqual(fim[1, 0], cov_vishid, places=2)
self.assertAlmostEqual(fim[2, 0], cov_visprod, places=2)
self.assertAlmostEqual(fim[1, 2], cov_hidprod, places=2)
def test_rbm_hamiltonian(self):
nvis, nhid = 10, 5
vishid = np.random.normal(size=(nvis, nhid))
model = IsingModel(nvis + nhid)
model.import_rbm01(nvis, nhid, np.zeros(nvis), np.zeros(nhid), vishid)
state = np.random.choice([True, False], size=nvis + nhid)
vis, hid = state[:nvis], state[nvis:]
energy = -np.dot(vis, np.dot(hid, vishid.T))
self.assertAlmostEqual(model.hamiltonian(state), energy)
