The Lincoln Continuous Tied-Mixture HMM Speech Recognizer*

The Lincoln Continuous Tied-Mixture HMM Speech Recognizer* Douglas B. Paul Lincoln Laboratory, MIT Lexington, Ma. 02173 Abstract The Lincoln robust HMM recognizer has been con- verted from a single Ganssian or Gaussian mixture pdf per state to tied mixtures in which a single set of Gaus- sians is shared between all states. There were some initial difficulties caused by the use of mixture pruning [12] but these were cured by using observation pruning. Fixed weight smoothing of the mixture weights allowed the use of word-boundary-context-dependent triphone models for both speaker-dependent (SD) and speaker- independent (SI) recognition. A second-differential ob- servation stream further improved SI performance but not SD performance. The overall recognition perfor- mance for both SI and SD training is equivalent to the best reported according to the October 89 Resource Management test set. A new form of phonetic context model, the semiphone, is also introduced. This new model significantly reduces the number of states required to model a vocabulary. Introduction Tied mixture (TM) HMM systems [3, 6] use a Gaus- sian mixture pdf per state in which a single set of Gaus- sians is shared among all states: Pi (0) ~- E Ci,j Gj (o) (1) 1 ci,j > O, E cij = l J where i is the arc or state, G i is the jth Gaussian, and o is the observation vector. This form of continuous obser- vation pdf shares the generality of discrete observation pdfs (histograms) with the absence of quantization error found in continuous density pdfs. Unlike the non-TM continuous pdfs, TM pdfs are easily smoothed with other pdfs by combining the mixture weights. Unlike discrete observation HMM systems, the Gaussians (analogous to the vector quantizer codebook of a discrete observation system) can be optimized simultaneously with the mix- ture weights. The training algorithms are identical to *This work was sponsored by the Defense Advanced Research Projects Agency. the algorithms for training a Gaussian mixture system except the Gaussians are tied across all arcs. Mixture and Observation Pruning Computing the full sum of equation 1 is expensive dur- ing training and prohibitively expensive during recogni- tion since it must be computed for each active state at each time step. (Because the word sequence is unknown, recognition has many more active states than does train- ing.) Ideally, one would only compute the terms which dominate the sum. However, it requires more computa- tion to find these terms than it does to simply sum them. Two faster approximate methods for reducing the com- putation exist: mixture and observation pruning. Mixture pruning simply drops terms that fall below a threshold during training. The weights may then be stored as a sparse array which also saves space. The computational savings are limited during the early it- erations of training since only a few terms have been dropped. The final SD distributions are quite sharp (i.e. have only a few terms), but the final SI distributions are quite broad (i.e. have many terms). Thus the savings are limited for …

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