I am trying to implement a trigram HMM tagger for a language that has over 1000 tags. In my training data I have 459 tags. Now if we consider that states of the HMM are all possible bigrams of tags, that would leave us with $459^2$ states and $(459^2)^2$ transitions between them, which would require a massive amount of memory.
Are there any workarounds around this? What I thought of is considering only bigrams seen in the data, but it is still a lot of memory.