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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.
You will want to keep track of the range of numbers that might have been chosen based on the answers that have been given so far until there is only one number left. You can approximately divide an integer by 2 by right-shifting it by one bit.
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