def _update_trans(self, elngamma, elnxi, n_obs):
for i in range(self.n_states):
for j in range(self.n_states):
numerator = -np.inf
denominator = -np.inf
for k in range(n_obs - 1):
numerator = elnsum(numerator, elnxi[i, j, k])
denominator = elnsum(denominator, elngamma[i, k])
self.trans[i, j] = eexp(elnproduct(numerator, -denominator))
def _update_emis(self, elngamma, obs_seq):
for e in range(self.emis.shape[0]):
for i in range(self.n_states):
numerator = -np.inf
denominator = -np.inf
for k in range(len(obs_seq)):
if obs_seq[k] - 1 == e:
numerator = elnsum(numerator, elngamma[i, k])
denominator = elnsum(denominator, elngamma[i, k])
self.emis[e, i] = eexp(elnproduct(numerator, -denominator))
def _update_init_eln(self, elngammas):
"""
This function calculate the update value of the initial probabilities as defined by the Berkeley notes references in the _m_step algorithm. It is the average of the sum of probabilities of x_1 over all sequences. i.e. the expected frequency of state Si at time t = 1
"""
for i in range(self.n_states):
numerator = -np.inf
denominator = 0
for idx in range(len(self.sequences)):
numerator = elnsum(numerator, elngammas[idx][i, 0])
denominator = denominator + 1
self.init[i] = eexp(numerator) / denominator
def _generate_gamma(self, elnalpha, elnbeta):
elngamma = np.zeros((self.n_states, self.n_obs + 1))
gamma = np.zeros((self.n_states, self.n_obs + 1))
for k in range(0, self.n_obs + 1):
norm = -np.inf
for i in range(self.n_states):
elngamma[i, k] = elnproduct(elnalpha[i, k], elnbeta[i, k])
norm = elnsum(norm, elngamma[i, k])
for i in range(self.n_states):
elngamma[i, k] = elnproduct(elngamma[i, k], -norm)
gamma[i, k] = eexp(elngamma[i, k])
return elngamma, gamma
def _update_emis_eln(self, elngammas):
"""
This function calculates the update of the transition probabilities as defined by the Berkeley notes references in the _m_step algorithm.
The numerator is the eln_xi values summed across all sequences and across all time steps.
The denominator is the eln_gamma values summed across all sequences and across all time steps.
"""
for e in range(self.emis.shape[0]):
for i in range(self.n_states):
numerator = -np.inf
denominator = -np.inf
for idx, obs_seq in enumerate(self.sequences):
for k in range(0, len(obs_seq)):
if obs_seq[k] == e:
numerator = elnsum(numerator, elngammas[idx][i, k])
denominator = elnsum(denominator, elngammas[idx][i, k])
self.emis[e, i] = eexp(elnproduct(numerator, -denominator))
def _update_trans_eln(self, gammas, xis):
"""
This function calculates the update of the transition probabilities as defined by the Berkeley notes references in the _m_step algorithm.
The numerator is the eln_gamma values summed across all sequences and across all time steps.
The denominator is the eln_gamma values summed across all sequences and across all time steps.
"""
for i in range(self.n_states):
for j in range(self.n_states):
numerator = -np.inf
denominator = -np.inf
for idx, obs_seq in enumerate(self.sequences):
for k in range(1, len(obs_seq)):
numerator = elnsum(numerator, elnxis[idx][i, j, k - 1])
denominator = elnsum(denominator,
elngammas[idx][i, k - 1])
self.trans[i, j] = eexp(elnproduct(numerator, -denominator))
def _eln_xi(self, elnalpha, elnbeta, obs_seq):
"""
This function calculates P(S_i_t, S_j_t+1) i.e. the probability of being in state S_i at time t and state S_j at time t+1.
"""
elnxi = np.zeros((self.n_states, self.n_states, len(obs_seq) - 1))
xi = np.zeros((self.n_states, self.n_states, len(obs_seq) - 1))
for k in range(len(obs_seq) - 1):
normalizer = -np.inf
for i in range(self.n_states):
for j in range(self.n_states):
elnxi[i, j, k] = elnproduct(
elnalpha[i, k],
elnproduct(
eln(self.trans.transpose()[i, j]),
elnproduct(eln(self.emis[obs_seq[k + 1], j]),
elnbeta[j, k + 1])))
normalizer = elnsum(normalizer, elnxi[i, j, k])
for i in range(self.n_states):
for j in range(self.n_states):
elnxi[i, j, k] = elnproduct(elnxi[i, j, k], -normalizer)
xi[i, j, k] = eexp(elnxi[i, j, k])
return elnxi, xi
def _update_init(self, elngamma):
for i in range(self.n_states):
self.init[i] = eexp(elngamma[i, 1])