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Consider the use of hidden Markov models for classifying sequences of four visible states, A-D. Train two hidden Markov models, each consisting of three hidden states (plus a null initial state and a null final state), fully connected, with the following data. Assume that each sequence starts with a null symbol and ends with an end null symbol (not listed).
Sample w1 w2
1 AABBCCDD DDCCBBAA
2 ABBCBBDD DDABCBA
3 ACBCBCD CDCDCBABA
4 AD DDBBA
5 ACBCBABCDD DADACBBAA
6 BABAADDD CDDCCBA
7 BABCDCC BDDBCAAAA
8 ABDBBCCDD BBABBDDDCD
9 ABAAACDCCD DDADDBCAA
10 ABD DDCAAA
(a) Print out the full transition matrices for each of the models.
(b) Assume equal prior probabilities for the two models and classify each of the following sequences: ABBBCDDD, DADBCBAA, CDCBABA, and ADBBBCD.
(c) As above, classify the test pattern BADBDCBA. Find the prior probabilities for your two trained models that would lead to equal posteriors for your two categories when applied to this pattern.
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