Editing Carnegie Mellon's Harpy System (section)

=== '''3. Data dependent transition probabilities''' ===
The Harpy system uses '''data-dependent transition probabilities'''. This is realized by heuristically calculate the transition probabilities for each state during the recognition process from speech-dependent knowledge, and only intrinsic '''phonemic durations''' in the Harpy system. 

The system uses '''minimum and maximum expected durations for each phone''' and the '''current duration''' of the states to calculate the transition probabilities. The current duration for a state is the number of time samples for which the state was its own best prior state. 

* The inter-state transition probability from a state is 1 if the current duration for that state is not less than the minimum expected duration for the phone of that state. If the current duration is less than the minimum expected, then the inter-state transition probability from that state is reduced by a heuristic amount that is proportional to the difference between the minimum expected and the actual current duration. If I is the minimum expected duration, C is the current duration (with C<I) then the inter-state transition probability is H<sup>I-C</sup> where H is a heuristic value. Similarly, if the current duration is not greater than the maximum expected duration, then the intra-state transition probability is 1, otherwise it is   where A is the maximum expected duration and C and H are as before. The current value used for H is.1. A value of 0 for H would be tantamount to a total rejection of a path should the state duration fall outside the interval between the minimum and maximum expected durations. A large value for H(close to 1) and a small interval between the minimum and maximum expected durations would produce a Gaussian like distribution for the transition probabilities.

{| class="wikitable"
|+
|'''Conditions'''
|'''Transition probability'''
|-
|The current duration ≥ The minimum expected duration
|1
|-
|The current duration < The minimum expected duration
|H<sup>I-C</sup>
|-
|The current duration ≤ The maximum expected duration
|1
|-
|The current duration > The maximum expected duration
|H<sup>C-A</sup>
|}