1
$\begingroup$

I am trying to use this equation

enter image description here

to calculate the alpha (forward) probabilities for the EM/Baum-welch algorithm but I'm running into some confusion. I don't understand what the $h_t$ is. I know its a hidden state, I have 16 different hidden states but don't know which one is $h_1$ for instance. Can I arbitrarily assign them an index or are they related to $v_t$?

I current have a transition matrix, emission matrix and an initial vector as well as some series of observed emissions.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
3
$\begingroup$

Perhaps the source of the confusion is your notation.

Usually, one defines the forward variables $α_j(t)$ as the probability of the partial observation sequence until time $t$, with state $S_j$ at time $t$ (reference).

Hence, under your notation, you use the forward procedure to calculate inductively $\alpha (h_t)$. If you have $T=16$ hidden states then you start at $\alpha (h_1)$ and finish at $\alpha (h_{16})$; each $\alpha (h_i)$ is a vector whose length is the number of total possible values the hidden states can take.

Improve this answer
$\endgroup$
2
  • $\begingroup$ I think I understand what your saying, so $h_1$ is just the initial vector (the probabilities of starting in each hidden state)? $\endgroup$
    – R-4
    Mar 29, 2017 at 12:26
  • $\begingroup$ Yes, it's a vector of the same length as $\alpha (h_i)$. it's usually known as the prior; supposed to reflect your "belief" regarding the probability of a hidden state accepting a certain value, before any evidence is taken into account. $\endgroup$
    – galoosh33
    Mar 29, 2017 at 12:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.