Replit: I tried to write HMM Forward function code:
```
# Write a function that performs the forward algorithm of an HMM. Ideally it uses numpy vectorization,
# But if you cannot do that it is fine too. Just perform forward inference, given HMM parameters and Observations.
# def HMM_forward() :
# Write your code here
# Hint:
# - Remember that HMMs are stochastic, so you will need to multiply transition matrices by observation probabilities
# - Remember that HMMs are stochastic, so you will need to multiply emission matrices by observation probabilities
# - Remember that HMMs are stochastic, so you will need to multiply emission matrices by transition matrices
# - Remember that HMMs are stochastic, so you will need to multiply emission matrices by transition matrices
# - Remember that HMMs are stochastic, so```
import numpy as np
def forward_algorithm(A, B, pi, obs):
"""
Performs the forward algorithm for an HMM.
Parameters:
A: numpy.ndarray, shape (N, N)
Transition matrix of the HMM, where N is the number of states.
B: numpy.ndarray, shape (N, M)
Emission matrix of the HMM, where M is the number of possible observations.
pi: numpy.ndarray, shape (N,)
Initial probability distribution over states.
obs: numpy.ndarray, shape (T,)
Sequence of T observations.
Returns:
alpha: numpy.ndarray, shape (T, N)
Forward probabilities for each state at each time step.
"""
T = obs.shape[0]
N = A.shape[0]
alpha = np.zeros((T, N))
alpha[0] = pi * B[:, obs[0]]
for t in range(1, T):
alpha[t] = np.dot(alpha[t-1], A) * B[:, obs[t]]
return alpha