HMM_Calc

Functions for generating Alpha and Delta tables from a Hidden Markov Model.

Parameters:

1. a: Matrix of transition probabilities. a[i][j] = a_{ij} = Probability of transitioning from state i to state j
2. b: Matrix of emission probabilities. b[i][x] = b_i(x) = Probability of emitting x at state i
3. pi: Array of start probabilities. pi[i] = pi_i = Probability of starting at state i
4. sequence: Array of integers corresponding to outputs. sequence[i] = The known output at time i

Example:

  # Transition properties
  # a[i][j] = probability of traveling to state j from state i
  a = [[0.3, 0.3, 0.4],
       [0.2, 0.7, 0.1],
       [0.2, 0.5, 0.3]]

  # Emission probabilities
  # b[i][x] = Probability of emitting output x at state i
  b = [[0.1, 0.0, 0.9],
       [0.3, 0.4, 0.3],
       [0.7, 0.2, 0.1]]

  # pi[i] = Probability of starting at state i
  pi = [0.2, 0.5, 0.3]

  # Observed output sequence
  sequence = [1, 2, 3, 1, 1, 4]

  # Prints alpha table and returns matrix
  alpha_table = alpha(a, b, pi, sequence)

  # Prints delta table and returns matrix
  delta_table = delta(a, b, pi, sequence)