I need to translate a training algorithm that involves sums and multiplications of probabilities to actual code. For that I need some sort of scaling procedure that allows me to avoid underflows, that is, misleading 0 probabilities.
A typical method is to apply the logs of probabilities but because of the sums this is not readily possible for my case. Another approach I saw in Rabiner's tutorial on HMMs, was his scaling procedure only dependent on t (time) applied to the forward algorithm and (the other way around) the backward algorithm, that when combined cancel each other to obtain the desired trained probabilities.
My question I wonder if there are books or text resources explaining common approaches to tackle the underflow problem that results in working with continuous multiplications of probabilities. Do you know any?
I hope I can get some ideas from that.