Problem

A hierarchical HMM is similar to the segment HMM, except that there is no explicit selection of the segment length. Rather, the HMM at a state calls a "subroutine" HMM Hs that defines the output at the state s; when the "subroutine" HMM enters a finish-state, the control returns to the top-level HMM, which then transitions to its next state. This hierarchical HMM (with three levels) is precisely the framework used as the standard speech recognition architecture.

a. Show how a three-level hierarchical HMM can be represented as a DBN.

b. Explain how you would modify the hierarchical HMM framework to deal with a motion tracking task, where, for example, the higher-level HMM represents motion between floors, the mid-level HMM motion between corridors, and the lowest-level HMM motion between rooms.