homework solutions for:

Homework #6:  Hidden Markov Modeling






submitted to:

Dr. Joseph Picone
ECE_8993 Fundamentals of Speech Recognition

September 24, 1998


submitted by:

Janna Shaffer








Department of Electrical and Computer Engineering
Mississippi State University
Box 9571, 216 Simrall, Hardy Rd.
Mississippi State, Mississippi 39762
Email: janna@cs.msstate.edu
Results
Training Data:
HHTTTHHHHTTTTTHHHHHHTTTTTTTHHHHHHHHTTTTTTTTTHHHHHHHHTTTTTTTH
HHHHHTTTTTHHHHTTTHHTHHTTHHHHHHHHHHTHHHHHTHHHHHHHHHHTHHHTHHHH
HHHHHHHHHTHHHHHHHHHTTHHHHHHTHHHTHHHHHTHHHHHHHHTHHHHHHTHTHHHH
HHHHHHHTTHHHHHHHHHHHHHHHTHHHHHTTHHHHHHHHHHTTHHHHHHHHHHHHHTTH
HHHHHHHHHHHTTHHHTHHHHHHHHHHHTHHHHHHTTHHHHHTHHHTHHHHHTHTHHHHH
THTHHHHHHHHHTHTHHHHHHTHTHHHHHTHTTHHHHHHHHHHHHHTHTHHHHHHHHHHH
HTHHHHHHHHHHHHHHHTHHHHHHHHHHHHHHHTHHHHHHHHHHTTHHHHHHHTHHHHHH
HHHHHTHHHHTHHHHHHHHHHTHHHHHHHHHHHHTTHHHHTTHHHHHHHHHHHHHHTTHH

Testing Data:
HTHTHTHTHTHTHTHTHTHT
HHHHHHHHHHHHHHHHHHHH
TTTTTTTTTTTTTTTTTTTT

Best Model:
Viterbi Training with 3 state 2 output symbol HMM
log P(O/M) = -97.957870 for the training data over 10 iterations
log P(O/M) = -20.189884 over the 3 testing sequences using the Viterbi algorithm for testing
	        log P(O[1]/M) (-10.874145): HTHTHTHTHTHTHTHTHTHT
        log P(O[2]/M) (-1.344210): HHHHHHHHHHHHHHHHHHHH
        log P(O[3]/M) (-7.971529): TTTTTTTTTTTTTTTTTTTT

From the training data, it is easy to see that the number of heads that occur outweigh the number of tails that will occur. Also, the tails that do occur, seem to do so in groups.  Therefore the second and third test sets should have the greater probability, which they do.