I am learning Hidden Markov Model and its implementation for Stock Price Prediction. I am trying to implement the Forward Algorithm according to this paper.
Here I found an implementation of the Forward Algorithm in Python.
import pandas as pd import numpy as np V = np.array([0, 1, 1, 2, 0, 1, 2, 0, 1, 0, 2]) # Transition Probabilities a = np.array(((0.54, 0.46), (0.49, 0.51))) # Emission Probabilities b = np.array(((0.16, 0.26, 0.58), (0.25, 0.28, 0.47))) # # Equal Probabilities for the initial distribution pi = np.array((0.5, 0.5)) def forward(V, a, b, pi): alpha = np.zeros((V.shape[0], a.shape[0])) alpha[0, :] = initial_distribution * b[:, V[0]] for t in range(1, V.shape[0]): for j in range(a.shape[0]): alpha[t, j] = alpha[t - 1].dot(a[:, j]) * b[j, V[t]] return alpha alpha = forward(V, a, b, pi) But it seems to me that it does not include (c) and (d) steps from the algorithm. So I added them:
def forward(V, a, b, pi): p = 1 alpha = np.zeros((V.shape[0], a.shape[0])) alpha[0, :] = pi * b[:, V[0]] for t in range(1, V.shape[0]): probability_of_observation = 0 #my code for j in range(a.shape[0]): alpha[t, j] = alpha[t - 1].dot(a[:, j]) * b[j, V[t]] probability_of_observation += alpha[t, j] #my code p = p * probability_of_observation #my code return p #changed p = forward(V, a, b, pi) #changed Does my code coincide with the given algorithm?
