1. EEL 6586: AUTOMATIC SPEECH PROCESSING Hidden Markov Model Lecture
Mark D. Skowronski
Computational Neuro-Engineering Lab
University of Florida
March 31, 2003

2. Questions to be Answered
What is a Hidden Markov Model?
How do HMMs work?
How are HMMs applied to automatic speech recognition?
What are the strengths/weaknesses of HMMs?

3. What is an HMM?
A Hidden Markov Model is a piecewise stationary model of a nonstationary signal.
Model parameters:
states -- represents domain of a stationary signal
interstate connections -- defines model architecture
pdf estimates (for each state)
Discrete -- codebooks
Continuous -- mean, covariance matrices

4. HMM Depiction

5. PDF Estimation Discrete Continuous
Codebook of feature space cluster centers
Probability for each codebook entry
Continuous
Gaussian mixtures (mean, covariance, mixture weights)
Discriminative estimates (neural networks)

6. How do HMMs Work? Three fundamental issues
Training: Baum-Welch algorithm
Scoring (evaluation): Forward algorithm
Optimal path: Viterbi algorithm
Complete implementation details:
“A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition”, L. R. Rabiner, IEEE Proceedings, Feb 1989

7. HMM Training Baum-Welch algorithm
Iterative procedure (on-line or batch mode)
Guaranteed to increase model accuracy after each iteration
Estimation may be model-based (ML) or discriminative (MMI)

8. HMM Evaluation Forward algorithm
Calculates P(O|λ) for ALL valid state sequences
Complexity:
order N2T, ~5000 computations
order 2T•NT (brute force), ~6E86 computations
N states, T speech frames

9. Optimal Path Viterbi algorithm
Determines the single most-likely state sequence for a given model and observation sequence
Dynamic programming solution
Likelihood of Viterbi path can be used for evaluation instead of Forward algorithm

10. HMMs in ASR
Piecewise stationary model of nonstationary signal
Type
# Models + -
Word
<1000
Coarticulation
Scaling
Phoneme 40
pdf estimation
Biphone
1400
Triphone
40K
TRADEOFF

11. Typical Implementations
Word models:
39 dimension feature vectors
3-15 states
1-50 Gaussian mixtures
Diagonal covariance matrices
First-order HMM
Single-step state transitions
Viterbi used for evaluation (speed)

12. Typical Implementations
Triphones
Left- and right-context phoneme
3-5 states
Up to 50 mixtures/state
40K models
39 dimension full covariance matrices
Approx 15 billion parameters to estimate
Approx 43,000 hours speech for training

13. Implementation Issues
Same number of states for each word model?
Underflow of evaluation probabilities?
Full/Diagonal covariance matrices?

14. HMM Limitations Piecewise stationary assumption iid assumption
Dipthongs
Tonal languages
Phonetic information in transitions
iid assumption
Slow articulators
Temporal information
No modeling beyond 100 ms time frame
Data intensive

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