If you align input feature vector sequence to HMM sequence each HMM state would have a region in the feature vector sequence. So you can calculate average length of those regions.
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I have another view of this subject. Please correct me if I am wrong.
Is this possible to calculate mean state duration using transition probabilities for a specific state. If I take all the occurences of this state in mdef file and its neighbouring state, then we can calculate average probabilities of that state. I mean to say, take average of transitional probabilities(to, from and self for that state) will it be equivalent to average state duration.
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This is an estimation, but pretty inaccurate one. HMM model doesn't describe state durations well so real state duration must be computed on a test data.
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The overall duration of the phoneme is reasonably well modeled by the
HMM. For the Bakis topology, no-skip HMM its modeled as a negative
binomial, and the model actually ends up appearing to fit the true
duration decently.
At the state level however, its not so clear. For one, we don't really
have a way of specifying what the states really are.
The individual states in the Bakis topology HMM have exponential
duration probability distributions -- P(n) = (1 - Tii)^n. You can
compute expectations etc. from them. But exponential distributions
are not great models for any single state, which are likely closer to
Pareto distributions -- you have to stay in the state for a minimum
duration. But the Markov model doesn't really have a way to enforce
pareto distributions, unless you make them significantly more complex.
I heard about the term "mean state durtion". Can anyone clear the term and also tell me how to calculate it?
If you align input feature vector sequence to HMM sequence each HMM state would have a region in the feature vector sequence. So you can calculate average length of those regions.
Thanks Nickolay for your input.
I have another view of this subject. Please correct me if I am wrong.
Is this possible to calculate mean state duration using transition probabilities for a specific state. If I take all the occurences of this state in mdef file and its neighbouring state, then we can calculate average probabilities of that state. I mean to say, take average of transitional probabilities(to, from and self for that state) will it be equivalent to average state duration.
This is an estimation, but pretty inaccurate one. HMM model doesn't describe state durations well so real state duration must be computed on a test data.
Thanks again.
The overall duration of the phoneme is reasonably well modeled by the
HMM. For the Bakis topology, no-skip HMM its modeled as a negative
binomial, and the model actually ends up appearing to fit the true
duration decently.
At the state level however, its not so clear. For one, we don't really
have a way of specifying what the states really are.
The individual states in the Bakis topology HMM have exponential
duration probability distributions -- P(n) = (1 - Tii)^n. You can
compute expectations etc. from them. But exponential distributions
are not great models for any single state, which are likely closer to
Pareto distributions -- you have to stay in the state for a minimum
duration. But the Markov model doesn't really have a way to enforce
pareto distributions, unless you make them significantly more complex.
-Bhiksha
On Wed, Feb 25, 2015 at 8:27 AM, Biswajit Das biswajit84@users.sf.net wrote:
--
Bhiksha Raj
Carnegie Mellon University
Pittsburgh, PA, USA
Tel: 412 268 9826