hmm training

gistfile1.py

# Created from these lecture notes:
# http://cseweb.ucsd.edu/classes/wi13/cse150-a/lecture/lecture11.pdf
# http://cseweb.ucsd.edu/classes/wi13/cse150-a/lecture/lecture12.pdf
# http://cseweb.ucsd.edu/classes/wi13/cse150-a/lecture/lecture13.pdf

# Dependencies:
#  init_{a,b,pi} := the initial estimated matrices, can be random
#  compute_forward := calculates the alpha matrix
#  compute_reverse := calculates the beta matrix
#  compute := calculates each of the matrices for the E-step
#  update := sums up over each of the observations, except for pi

def learn(obs):
   # default values or random
   a, b, pi = init_a, init_b, init_pi 
   n_iters = 100000 # is there a better condition I could check?
   while n_iters > 0:
      # E-step
      alpha = compute_forward(a, b, pi, obs)
      beta = compute_reverse(a, b, pi, obs)
      # the derivations in the notes don't use pi, but I derived 
      #   P(S_1=i, O_{1..T}) = pi[i]*b[i,obs[1]]*beta[i,1]
      # the notes state prob_i is the sum of each column in prob_ij
      prob_ij, prob_i, prob_1 = compute(alpha, beta, a, b, obs, pi)

      # M-step
      a, b, pi = update(prob_ij, prob_i, prob_1)
   return a, b, pi