In the sources I consulted it states that in the Baum Welch algorithm the reestimate of the initial probability of state $i$ of the HMM is $\pi^*_i = \gamma_i(1)$. But $\gamma_i(t)$ is the probability of being in state ${\displaystyle i}$ at time ${\displaystyle t}$ given the observed sequence ${\displaystyle Y}$ and the parameters ${\displaystyle \theta }$ (quote wiki)So, then why does this probability not need to be normalised like so? :$$\pi^*_i = \frac{\gamma_i(1)}{\sum_{j = 1}^N \gamma_j(1)}$$After all normalizing is what is done for the reestimate of the transition probabilities and the emission probabilities too.
Hidden Markov Model initial probability reestimate: Why $\pi^*_i = \gamma_i(1)$ instead of $\pi^*_i = \frac{\gamma_i(1)}{\sum_{j = 1}^N \gamma_j(1)}$
machine learning;probability theory;probabilistic algorithms;hidden markov models
It is defined to be a probability.  A probability is by definition already normalized.  In particular, we are guaranteed that$$\sum_{j=1}^N \gamma_j(1) = 1,$$as there are only $N$ possibilities for the state that you're in at time $1$, and these $N$ cases have no overlap.