def partial_EM(self, data, cond_muh_ijk, indices, weights=None, eps=1e-4, maxiter=10, verbose=0):
(i, j, k) = indices
converged = False
previous_L = utilities.average(
self.likelihood(data), weights=weights) / self.N
mini_epochs = 0
if verbose:
print('Partial EM %s, L = %.3f' % (mini_epochs, previous_L))
while not converged:
if self.nature in ['Bernoulli', 'Spin']:
f = np.dot(data, self.weights[[i, j, k], :].T)
elif self.nature == 'Potts':
f = cy_utilities.compute_output_C(data, self.weights[[i, j, k], :, :], np.zeros([
data.shape[0], 3], dtype=curr_float))
tmp = f - self.logZ[np.newaxis, [i, j, k]]
tmp -= tmp.max(-1)[:, np.newaxis]
cond_muh = np.exp(tmp) * self.muh[np.newaxis, [i, j, k]]
cond_muh /= cond_muh.sum(-1)[:, np.newaxis]
cond_muh *= cond_muh_ijk[:, np.newaxis]
self.muh[[i, j, k]] = utilities.average(cond_muh, weights=weights)
self.cum_muh = np.cumsum(self.muh)
self.gh[[i, j, k]] = np.log(self.muh[[i, j, k]])
self.gh -= self.gh.mean()
if self.nature == 'Bernoulli':
self.cond_muv[[i, j, k]] = utilities.average_product(
cond_muh, data, mean1=True, weights=weights) / self.muh[[i, j, k], np.newaxis]
self.weights[[i, j, k]] = np.log(
(self.cond_muv[[i, j, k]] + eps) / (1 - self.cond_muv[[i, j, k]] + eps))
self.logZ[[i, j, k]] = np.logaddexp(
0, self.weights[[i, j, k]]).sum(-1)
elif self.nature == 'Spin':
self.cond_muv[[i, j, k]] = utilities.average_product(
cond_muh, data, mean1=True, weights=weights) / self.muh[[i, j, k], np.newaxis]
self.weights[[i, j, k]] = 0.5 * np.log(
(1 + self.cond_muv[[i, j, k]] + eps) / (1 - self.cond_muv[[i, j, k]] + eps))
self.logZ[[i, j, k]] = np.logaddexp(
self.weights[[i, j, k]], -self.weights[[i, j, k]]).sum(-1)
elif self.nature == 'Potts':
self.cond_muv[[i, j, k]] = utilities.average_product(
cond_muh, data, c2=self.n_c, mean1=True, weights=weights) / self.muh[[i, j, k], np.newaxis, np.newaxis]
self.cum_cond_muv[[i, j, k]] = np.cumsum(
self.cond_muv[[i, j, k]], axis=-1)
self.weights[[i, j, k]] = np.log(
self.cond_muv[[i, j, k]] + eps)
self.weights[[i, j, k]] -= self.weights[[i, j, k]
].mean(-1)[:, :, np.newaxis]
self.logZ[[i, j, k]] = utilities.logsumexp(
self.weights[[i, j, k]], axis=-1).sum(-1)
current_L = utilities.average(
self.likelihood(data), weights=weights) / self.N
mini_epochs += 1
converged = (mini_epochs >= maxiter) | (
np.abs(current_L - previous_L) < eps)
previous_L = current_L.copy()
if verbose:
print('Partial EM %s, L = %.3f' % (mini_epochs, current_L))
return current_L
def likelihood(self, data):
if data.ndim == 1:
data = data[np.newaxis, :]
if self.nature in ['Bernoulli', 'Spin']:
f = np.dot(data, self.weights.T)
elif self.nature == 'Potts':
f = cy_utilities.compute_output_C(data, self.weights, np.zeros(
[data.shape[0], self.M], dtype=curr_float))
return utilities.logsumexp((f - self.logZ[np.newaxis, :] + np.log(self.muh)[np.newaxis, :]), axis=1)
def likelihood_and_expectation(self, data):
if self.nature in ['Bernoulli', 'Spin']:
f = np.dot(data, self.weights.T)
elif self.nature == 'Potts':
f = cy_utilities.compute_output_C(data, self.weights, np.zeros(
[data.shape[0], self.M], dtype=curr_float))
L = utilities.logsumexp(
(f - self.logZ[np.newaxis, :] + np.log(self.muh)[np.newaxis, :]), axis=1)
cond_muh = np.exp(
f - self.logZ[np.newaxis, :]) * self.muh[np.newaxis, :]
cond_muh /= cond_muh.sum(-1)[:, np.newaxis]
return L, cond_muh
def expectation(self, data):
if data.ndim == 1:
data = data[np.newaxis, :]
if self.nature in ['Bernoulli', 'Spin']:
f = np.dot(data, self.weights.T)
elif self.nature == 'Potts':
f = cy_utilities.compute_output_C(data, self.weights, np.zeros(
[data.shape[0], self.M], dtype=curr_float))
tmp = f - self.logZ[np.newaxis, :]
tmp -= tmp.max(-1)[:, np.newaxis]
cond_muh = np.exp(tmp) * self.muh[np.newaxis, :]
cond_muh /= cond_muh.sum(-1)[:, np.newaxis]
return cond_muh
def bilinear_form(W, X1, X2, c1=1, c2=1):
xshape = X1.shape
X1, xdim = reshape_in(X1, xdim=1)
X2, xdim = reshape_in(X2, xdim=1)
if (c1 == 1) & (c2 == 1):
out = np.sum(X1 * np.tensordot(X2, W, axes=(-1, 1)), -1)
elif (c1 == 1) & (c2 > 1):
out = np.sum(
X1 * cy_utilities.compute_output_C(
X2, W, np.zeros(X1.shape, dtype=curr_float)), -1)
elif (c1 > 1) & (c2 == 1):
out = cy_utilities.dot_Potts2_C(
X1.shape[1], c1, X1, np.tensordot(X2.astype(curr_float), W,
(1, 1)))
elif (c1 > 1) & (c2 > 1):
out = cy_utilities.bilinear_form_Potts_C(X1, X2, W)
return reshape_out(out, xshape, xdim=1)