# Many values of HMM matrices, A and B, tend to zero

I'm experimenting with an HMM. I have a sequence of observations (10000) and the original matrices A,B and pi that generated those observations. There are 4 types of observations.

What I am trying to do is to train a randomly initialized HMM (initial distributions are near uniform) with different numbers of states in order to see its behavior for numbers of states lower or higher than the one that generated them.

The original model that generated the observations had 3 states.

I observed that for a number 7 or more states a lot of the matrices' values tend to zero. Is there some explanation for the reason why this would happen?

I'm not trying to find why it is happening specifically in my case. I'm not trying to solve a problem of mine.

I'm in fact curious to find whether this is something that happens in general and there is some explanation behind this.

Thank you.

Suppose you have transition matrix $A$ is $7 \times 7$ and emission matrix $B$ is $7 \times 4$ (assume you have 4 different types of observations), that is $7+7\times7+7\times4=84$ parameters, to fit such a model, it is better to have a sequence with thousands of observations.