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EEL 6586: AUTOMATIC SPEECH PROCESSING Hidden Markov Model Lecture

EEL 6586: AUTOMATIC SPEECH PROCESSING Hidden Markov Model Lecture. Mark D. Skowronski Computational Neuro-Engineering Lab University of Florida March 31, 2003. Questions to be Answered. What is a Hidden Markov Model? How do HMMs work? How are HMMs applied to automatic speech recognition?

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EEL 6586: AUTOMATIC SPEECH PROCESSING Hidden Markov Model Lecture

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  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 • 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 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 • Dipthongs • Tonal languages • Phonetic information in transitions • iid assumption • Slow articulators • Temporal information • No modeling beyond 100 ms time frame • Data intensive

  15. Download Slides www.cnel.ufl.edu/~markskow/papers/hmm.ppt

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