Hierarchical General Hidden Markov Model Plugin - Variable Batch

The Hierarchical General Hidden Markov Model - Variable Batch (HMM-VarBatch) plugin is a generalized version of the HMM-Batch one, and was implemented during the work of [#!carolina2007!#]. Inside each hidden state, the user defines a general Markov chain with an absorbing state, which is responsible for the symbol emissions. Figure illustrates the structure of such a hierarchical model.

Figure: Example of a hierarchical general HMM with variable batch size, $2$ hidden states and $4$ observation symbols. Notice the absorbing state, which is identified by the dashed dark circle.

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 through its states, until it reaches the absorbing state, which, then, causes the upper-level chain to make another transition^11.11. 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.

Important: It is crucial to keep in mind that the absorbing state also emits one symbol, which we call the end of batch symbol. This symbol is part of the observation symbols, just like every other, and, thus, must be part of the observations collected. All trace files used with this plugin must end with this symbol, since it represents the end of a batch of observations within some hidden state.