An Initial Study on Minimum Phone Error Discriminative Learning of Acoustic Model for Mandarin Large

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An Initial Study on Minimum Phone Error
Discriminative Learning of Acoustic Model for
Mandarin Large Vocabulary Continuous Speech
Recognition

• Jen-Wei Kuo
• National Taiwan Normal University

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Outline

• Minimum Phone Error (MPE) Training
• Objective Function From Minimum Overall Risk
• Function Maximization
• Update Formula
• MAP updates (I-Smoothing)
• MPE Linear Transform based Adaptation
• Model Space Adaptation (MPE-LR)
• Feature Space Adaptation (MPE-LT)
• Experiments

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Notations
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Minimum Overall Risk
Loss function
Overall risk
Classifier Design Conventional MAP
decoding, Hypothesis tesing, WER minimization
(Sausage), MBR Recognition
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Overall Risk Criterion Estimation

• ORCE was firstly proposed by Na Eurospeech 95,
  using the zero-one loss function.
• Kaiser introduced the Levenshtein distance to be
  as the loss function in ORCE ICSLP00,
  SpeechComm02.

average loss of all hypotheses
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Maximize the average accuracy

• ORCE can be regarded as maximizing the average
  accuracy of all possible hypotheses.
• It would try to increase the weight of the path
  with higher accuracy, and reduce the weight of
  the lower one.
• The higher/lower accuracy the path has, the more
  positive/negitive contribution it gives.

average accuracy of all hypotheses
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Minimum Phone Error (MPE)

• The improvements from ORCE to MPE
• The use of lattices
• MAP estimation of parameters (I-smoothing)
• The set of the smoothing constants in the EB
  update equations
• The emphasis on phone error rather than word
  error

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Expectation Maximum
Berlin Chen
How to do?
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Lower Bound
Construct a tractable lower bound
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Three Steps for EM

• Step 1.Draw a lower bound
• Use the Jensens inequality
• Step 2.Find the best lower bound
• Let the lower bound touch the objective function
  at current guess
• Step 3.Maximize the best lower bound
• Obtain the new guess
• Go to Step 1 until converge

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Step 1.Draw a lower bound
Apply Jensens Inequality
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Step 2.Find the best lower bound

• Let the lower bound touch the objective function
  at current guess
• Find the best at

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Step 2.Find the best lower bound
Set it to zero
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Step 2.Find the best lower bound
Q function
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Strong-sense auxiliary function

• e.g. EM algorithm
• 
  

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Weak-sense auxiliary function and smooth function

• Weak-sense auxiliary function
• Smooth function

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Weak-sense auxiliary function for MPE
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Weak-sense auxiliary function for MPE
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Weak-sense auxiliary function for MPE
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Weak-sense auxiliary function for MPE
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EBW equivalent smooth function
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EBW equivalent smooth function
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MAP updates (I-smoothing)
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Experiments -Baseline

• Character error rate for ML training

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Experiments

• Character error rate on different settings