Phone HMM within embedded training

[Siqi S]

In embedding training, would one specific phone HMM be shared across words if the same phone occurred in multiple words in one sentence? Including both the A matrix and the Gaussian parameters?

[Simon]

Yes, that’s correct – shared across all occurrences of that phone in the entire training data. We train one phone model on all available examples.

The implementation of this involves performing the E step for all data, “accumulating” (i.e., adding up) the necessary statistics (in fact we “accumulate” all the numerators and denominators of the M step equations, but don’t yet divide one by the other). Once all of that has been accumulated across the training data, the M step updates the model’s parameters. There is one numerator accumulator and one denominator accumulator for every individual model parameter (e.g., for the mean of each and every Gaussian).

(This implementation detail is not examinable for Speech Processing.)

[Siqi S]

Thank you for the clarification. During decoding, in hierarchical full graph, some phone HMM also occurs in several word (e.g. [ow] in “zero” and “oh” in Fig 9.22 in Jurafsky’s book). Are the A matrix and Gaussian parameters also shared among the occurrences?

[Simon]

Yes – there is only one model per phone (in the case of monophone models).

[Author]

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