def _em(self, trans, states):
'''
Perform parameter estimation for a hidden Markov model (HMM).
Perform parameter estimation for an HMM using multi-dimensional Gaussian
states. The training observation sequences, signals, are available
to the class, and states designates the initial allocation of emitting states to the
signal time steps. The HMM parameters are estimated using Viterbi
re-estimation.
Note: It is possible that some states are never allocated any
observations. Those states are then removed from the states table, effectively redusing
the number of emitting states. In what follows, n_states is the original
number of emitting states, while n_states' is the final number of
emitting states, after those states to which no observations were assigned,
have been removed.
Parameters
----------
trans : (n_states+1,n_states+1) ndarray
The left-to-right transition probability table. The rightmost column contains probability
of transitioning to final state, and the last row the initial state's
transition probabilities. Note that all the rows need to add to 1.
states : (n_obs, n_states) ndarray
Initial allocation of signal time-steps to states as a one-hot encoding. Thus
'states[:,j]' specifies the allocation of all the observations to state j.
Return
------
trans : (n_states'+1,n_states'+1) ndarray
Updated transition probability table
dists : (n_states',) list
Gaussian object of each component.
newLL : float
Log-likelihood of parameters at convergence.
iters: int
The number of iterations needed for convergence
'''
covs, means = self._updatecovs(states) # Initialize the covariances and means using the initial state allocation
dists = [Gaussian(mean=means[i], cov=covs[i]) for i in range(len(covs))]
oldstates, trans, oldLL = self._calcstates(trans, dists)
converged = False
iters = 0
while not converged and iters < self.maxiters:
covs, means = self._updatecovs(oldstates)
dists = [Gaussian(mean=means[i], cov=covs[i]) for i in range(len(covs))]
newstates, trans, newLL = self._calcstates(trans, dists)
if abs(newLL - oldLL) / abs(oldLL) < self.rtol:
converged = True
oldstates, oldLL = newstates, newLL
iters += 1
if iters >= self.maxiters:
warn("Maximum number of iterations reached - HMM parameters may not have converged")
return trans, dists, newLL, iters
def __init__(self, data, n_mix, sigma_min=0.1, sigma_max=1.0):
self.data = data
mu_min = min(data)
mu_max = max(data)
# create n-gaussians that will comprise the gaussian mixture model
self.gaussians = {}
# probability of each gaussians
self.mix = {}
# number of gaussians
self.n_mix = n_mix
# initialize the gaussians
for i in range(0, n_mix):
self.gaussians[i] = Gaussian(uniform(mu_min, mu_max),
uniform(sigma_min, sigma_max))
self.mix[i] = 1/n_mix
