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So, if I model observation probability for a given hidden state according to a multivariate gaussian mixture model, then which parameters need to be initialized random to perform parameter re-estimation via a variation of Baum-Welch algorithm?

I know that the initial distributions $\pi(i)$ has to be initialized random given sum of $\pi(i)$ for all $i$ is 1, and so does the transition probability $a(i,j)$, given sum of $a(i,j)$ for all $j$ is 1.

And I do know that the mean vector also has to be initialized random as well as the mixture weights.

Question: Should I also randomly initialize the covariance vector?

Or should I compute the covariance matrix given the randomly initialized mean vector?

(The latter being the most likely in my opinion.)

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