Forward algorithm written by ruby

Hidden Markov Model has three problems:

1) estimation problem: given an observation sequence o = o1o2... OT and model u = (a, B, π), how to quickly calculate the probability of observing the sequence o under the given model u, that is, P (o | U)

2) sequence problem: Given the observation sequence o = o1o2... OT and model u = (a, B, π), how to quickly and effectively select the "Optimal" state sequence q = q1q2... qt, so that the state sequence is "best interpreted" to observe the sequence?

3) Training problem or parameter estimation: given an observation sequence o = o1o2... ot, how can we obtain the model parameter value based on the maximum likelihood estimation? That is, how to adjust the parameters of Model U = (a, B, π) to make P (o | u) The largest?

Question 1 is a decoding problem. forward algorithms can solve this problem (Forward procedure) and are also an application of dynamic programming.

For more information about the forward algorithm, see the following article.

Http://www.cnblogs.com/tornadomeet/archive/2012/03/24/2415583.html

Ruby code

 

class FowardAlgorithm  def initialize(pi, trans_pro, emit_pro)    @pi = pi    @trans_pro = trans_pro    @emit_pro = emit_pro  end  def alpha1(state, ob)    @pi[state] * @emit_pro[state][ob]  end  def alpha(t, state)    # t starts from 0, states starts from 9    if t.equal? 0      alpha1(state, @ob[0])    else      sum = ([email protected]_pro.size).inject(0.0) { |sum, i| sum += alpha(t-1, i) * @trans_pro[i][state] }      sum * @emit_pro[state][@ob[t]]    end  end  def p_rerial_n ob    n = ob.size    n -= 1    @ob = ob    # time & states    res = 0.0    [email protected]_pro.size.times { |i|      #print "time #{n}, state #{i}"      tmp = alpha n, i      res += tmp    }    res  endenddef test  pi = [0.2, 0.4, 0.4]  trans_pro = [      [0.5, 0.2, 0.3],      [0.3, 0.5, 0.2],      [0.2, 0.3, 0.5]  ]  emit_pro = [      [0.5, 0.5],      [0.4, 0.6],      [0.7, 0.3]  ]  f = FowardAlgorithm.new pi, trans_pro, emit_pro  puts f.p_rerial_n([0, 1, 0, 1])endif $PROGRAM_NAME == __FILE__  testend