HMM.py

import numpy as np

class HMM : 
    """
    Given an input Sequence and a HMM ie the set containing Transition probabilitites,
    Emission probabilitites, No of Hidden States and Emitted states, evaluate the probability 
    of the sequence
    """
    def __init__(self,Transition_prob,Emission_prob,N_states,N_emitted_states):
        self.Transition_prob = Transition_prob
        self.Emission_prob = Emission_prob
        self.N_states = N_states
        self.N_emitted_states = N_emitted_states
        
    
    def forward_algorithm_matrix(self,Sequence,initial_proba):
        
        Tp = self.Transition_prob
        Ep = self.Emission_prob
        NHstates = self.N_states
        NEstates = self.N_emitted_states

        # Initialization 
        state_M = np.zeros((len(NHstates),len(Sequence[0])+1))
        state_M[:,:1] = initial_proba.reshape(len(NHstates),1)

        # Forward Algorithm
        for i in range(len(Sequence.T)):   
            state_M[:,i+1] = (Tp.T * Ep[:,Sequence.T[i]]) @ state_M[:,i]
        
        # Termination 
        return state_M
    
    def evaluate_sequence(self,Sequence,initial_proba):
    
        computed_M = self.forward_algorithm_matrix(Sequence,initial_proba)
        
        return np.sum(computed_M[:,-1])
    
    def vitterbi_algorithm_matrix(self,Sequence,initial_proba):
        
        Tp = self.Transition_prob
        Ep = self.Emission_prob
        NHstates = self.N_states
        NEstates = self.N_emitted_states
        
        # Initialization 
        state_M = np.zeros((len(NHstates),len(Sequence[0])+1))
        state_M[:,:1] = initial_proba.reshape(len(NHstates),1)

        # Forward Algorithm
        for i in range(len(Sequence.T)): 
            most_prob_state, max_prob = np.argmax(state_M[:,i]), np.max(state_M[:,i])
            state_M[:,i+1] = (T[most_prob_state,:]*E[:,most_prob_state])*max_prob            
        
        return state_M
    
    def decode_sequence(self,Sequence,initial_proba):
        
        vitterbi_matrix = self.vitterbi_algorithm_matrix(Sequence,initial_proba)
        traceback = np.zeros_like(vitterbi_matrix)
        traceback[vitterbi_matrix.argmax(0),np.arange(len(vitterbi_matrix[0]))] = 1
        states = np.array(['W'+ str(traceback[:,i].argmax()) for i in range(len(traceback[0]))],dtype=object)
        
        states_dict = {'Hidden_states' : states, 'Traceback':traceback}
        
        return states_dict