def get_forward_backward(self, data):
pcond = [None] * (len(data) - 1)
forward = [None] * len(data)
backward = [None] * len(data)
mu = np.repeat(np.repeat(self.mu, self.nbc_u, axis=0),
self.nbc_u,
axis=1)
sigma = np.repeat(np.repeat(self.sigma, self.nbc_u, axis=0),
self.nbc_u,
axis=1)
forward[0] = np.sum(np.multiply(
(self.t.T * self.p).T,
np_multivariate_normal_pdf_marginal(data[0], mu, sigma,
(len(data[0]) - 1))),
axis=1)
forward[0] = forward[0] / np.sum(forward[0])
backward[len(data) - 1] = np.array([1] * self.t.shape[0])
for l in range(1, len(data)):
k = len(data) - 1 - l
if pcond[l - 1] is None:
auxpb = np.multiply(
(self.t.T * self.p).T,
np_multivariate_normal_pdf(data[l - 1:l + 1].flatten(), mu,
sigma))
auxpb2 = np.sum(np.multiply(
(self.t.T * self.p),
np_multivariate_normal_pdf_marginal(
data[l - 1], mu, sigma, (len(data[l - 1]) - 1))),
axis=1)
pcond[l - 1] = (auxpb.T / auxpb2).T
if pcond[k] is None:
auxpb = np.multiply(
(self.t.T * self.p).T,
np_multivariate_normal_pdf(data[k:k + 2].flatten(), mu,
sigma))
auxpb2 = np.sum(np.multiply(
(self.t.T * self.p).T,
np_multivariate_normal_pdf_marginal(
data[k], mu, sigma, (len(data[k]) - 1))),
axis=1)
pcond[k] = (auxpb.T / auxpb2).T
forward[l] = np.dot(pcond[l - 1].T, forward[l - 1])
forward[l] = forward[l] / np.sum(forward[l])
backward[k] = np.dot(pcond[k], backward[k + 1])
backward[k] = backward[k] / np.sum(backward[k])
return forward, backward, pcond
def generate_sample(self, length, dimY):
hidden = [None] * length
visible = [None] * length
cls = [a.flatten() for a in np.indices(self.t.shape)]
test = np.random.multinomial(1, (self.t.T * self.p).T[cls[0], cls[1]])
hidden[0] = cls[0][test.tolist().index(1)]
hidden[1] = cls[1][test.tolist().index(1)]
v = multivariate_normal.rvs(self.mu[hidden[0], hidden[1]],
self.sigma[hidden[0],
hidden[1]]).reshape(-1, dimY)
visible[0] = v[0].tolist()
visible[1] = v[1].tolist()
for i in range(2, length):
auxpb = np.multiply(
(self.t.T * self.p).T,
np_multivariate_normal_pdf_marginal(visible[i - 1], self.mu,
self.sigma, (dimY - 1)))
pcond = (auxpb.T / np.sum(auxpb, axis=1)).T
test = np.random.multinomial(1, pcond[hidden[i - 1], :])
hidden[i] = test.tolist().index(1)
mean = self.mu[hidden[i - 1], hidden[i]][dimY:] + self.sigma[
hidden[i - 1], hidden[i]][:dimY, dimY:] @ (
self.sigma[hidden[i - 1], hidden[i]][dimY:, dimY:]
@ np.linalg.inv(self.sigma[hidden[i - 1],
hidden[i]][:dimY, :dimY])
) @ (visible[i - 1] - self.mu[hidden[i - 1], hidden[i]][:dimY])
cov = self.sigma[hidden[i - 1], hidden[i]][dimY:, dimY:] @ np.sqrt(
1 - (self.sigma[hidden[i - 1], hidden[i]][:dimY, dimY:]
@ self.sigma[hidden[i - 1], hidden[i]][:dimY, dimY:]))
visible[i] = multivariate_normal.rvs(mean,
cov).reshape(dimY).tolist()
return np.array(hidden), np.array(visible)
def simul_hidden_apost(self, data, backward, pcond):
res = [None] * len(data)
aux = np.sum(np.multiply(
(self.t.T * self.p).T,
np_multivariate_normal_pdf_marginal(data[0], self.mu, self.sigma,
(len(data[0]) - 1))),
axis=1) * backward[0]
test = np.random.multinomial(1, aux / np.sum(aux))
res[0] = test.tolist().index(1)
for i in range(1, len(data)):
aux = pcond[i - 1] * backward[i]
aux = (aux.T / (backward[i - 1] * np.sum(aux))).T
test = np.random.multinomial(
1, aux[res[i - 1]] / np.sum(aux[res[i - 1]]))
res[i] = test.tolist().index(1)
return np.array(res)
