Hierarchical General Hidden Markov Model Plugin - Fixed Batch

The Hierarchical General Hidden Markov Model - Fixed Batch (HMM-Batch) plugin is a generalized version of the GHMM one, and was implemented during the work of [#!carolina2007!#]. Inside each state, instead of a simple Gilbert model, the user can define a general Markov chain, which, as in the case of the GHMM, is responsible for the symbol emissions. Figure illustrates the structure of such a hierarchical model.

Figure: Example of a hierarchical general HMM with 2 hidden states and 4 observation symbols.

After each transition $(S_i, S_j)$ in the the hidden chain (the upper-level one), the lower-level model associated with $S_j$ emits symbols by transiting for a fixed number of steps, called a batch, before the upper-level chain makes another transition^11.10. Every time the lower-level Markov chain makes one transition, thus reaching one of its states, the model emits one symbol, which is the one associated with the lower-level state just reached. Hence, symbol $k$ is emitted every time the lower-level state $I_k$ is reached, where $I_k$, with $k =\{0, \dots, M-1\}$, defines a lower-level state inside the hidden state $S_j$. Each lower-level state emits one, and only one, symbol, and different lower-level states, inside a same hidden state, cannot both emit the same symbol.