ASR

1
Design Issues in HMMs for ASR

• Model Topology
• Gaussian Distributions
• Independence vs. non-independence
• Variance vs. covariance
• Gaussian State Emission Distributions
• Gaussian Mixtures
• Tied State Distributions
• Speech Parametrisation with HMMs

2
HMM Topology

• Left-right model suitable for speech
• Can use arcs that skip states. Why?

3
Phones HMM States

• Rule of thumb
• 1 state per phone
• 1 state per subphone unit
• Continuous speech
• Usually use subphone models
• Mixture densities for state emissions
• Tied states

4
Independence Variance
Bivariate data with independent distributions and
similar variances
5
Independence Variance
Bivariate data with independent distributions and
different variances
6
Non-independence Covariance
Bivariate data with non-independent
distributions, i.e. with covariance
7
Non-independence Covariance
Negative covariance
8
Calculating Observation Emission Probabilities

• Univariate (1-dimensional observation)

• Multivariate (n-dimensional observation)

9
Gaussian Mixtures for Multimodal Distributions
10
Tied State Distributions

• Tie together states whose acoustic emissions
  should be similar
• Example triphones ten, tep, ken
• If triphone models have 3 states each, which
  states should we tie?
• Tying allows us to make most effective use of
  available data
• See silence and short-pause models in the HTK
  book

11
Speech Parametrisation with HMMs

• Can use delta and acceleration coefficients
• Average over a number of frames
• Discrete emission probability distributions
• Vector quantisation
• Use perceptually motivated representations whose
  multivariate distributions tend to be independent
  (zero covariance)
• MFCCs, PLP
• Assume zero covariance
• Considerably reduces computation
• Given a diagonal matrix
• what is its inverse?
• What is its determinant?