Python Implementation of Viterbi Algorithm

Question

I\'m doing a Python project in which I\'d like to use the Viterbi Algorithm. Does anyone know of a complete Python implementation of the Viterbi algorithm? The correctness

Answer 1

I have modified @Rhubarb's answer for the condition where the marginal probabilities are already known (e.g by computing the Forward Backward algorithm).

def viterbi (transition_probabilities, conditional_probabilities):
    # Initialise everything
    num_samples = conditional_probabilities.shape[1]
    num_states = transition_probabilities.shape[0] # number of states

    c = np.zeros(num_samples) #scale factors (necessary to prevent underflow)
    viterbi = np.zeros((num_states,num_samples)) # initialise viterbi table
    best_path_table = np.zeros((num_states,num_samples)) # initialise the best path table
    best_path = np.zeros(num_samples).astype(np.int32) # this will be your output

    # B- appoint initial values for viterbi and best path (bp) tables - Eq (32a-32b)
    viterbi[:,0] = conditional_probabilities[:,0]
    c[0] = 1.0/np.sum(viterbi[:,0])
    viterbi[:,0] = c[0] * viterbi[:,0] # apply the scaling factor

    # C- Do the iterations for viterbi and psi for time>0 until T
    for t in range(1, num_samples): # loop through time
        for s in range (0,num_states): # loop through the states @(t-1)
            trans_p = viterbi[:, t-1] * transition_probabilities[:,s] # transition probs of each state transitioning
            best_path_table[s,t], viterbi[s,t] = max(enumerate(trans_p), key=operator.itemgetter(1))
            viterbi[s,t] = viterbi[s,t] * conditional_probabilities[s][t]

        c[t] = 1.0/np.sum(viterbi[:,t]) # scaling factor
        viterbi[:,t] = c[t] * viterbi[:,t]

    ## D - Back-tracking
    best_path[num_samples-1] =  viterbi[:,num_samples-1].argmax() # last state
    for t in range(num_samples-1,0,-1): # states of (last-1)th to 0th time step
        best_path[t-1] = best_path_table[best_path[t],t]
    return best_path