1
$\begingroup$

Given a transition matrix, starting probability, means and covariances

Is it possible to predict the most likely observed sequence for a given state sequence using the above details? If yes, how?

Thanks in advance.

$\endgroup$
2
$\begingroup$

Yes; this is just the expected value with respect to $P(Y|M, S)$ where $Y$ is the observed sequence, $M$ represents the parameters of the HMM, and $S$ is the given state sequence. Since your state sequence is given, you don't even need the transition matrix or starting probabilities; we're only interested in the part of the model that generates the observations (probably a Gaussian given your description). So, assuming univariate observations:

$$P(Y|M,S) = \prod_i^N \mathbb{N}(y_i|\mu_{s_i}, \sigma_{s_i})$$

where $s_i$ is the state for observation $i$ in the sequence. As we know, the expected value of a Gaussian is just its mean value, so the most likely observed sequence Y is the sequence $\{\mu_{s_1}, ... , \mu_{s_N}\}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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