Minimum Phone Error (MPE)Model and Feature Training

ShihHsiang 2006

2

The derivation flow of the various training criteria

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3

Difference

• MPE v.s. ORCE– ORCE focuses on word error rate and is implemented on N-best res

ults– MPE focuses on phone accuracy and is implemented on a word gra

ph also introduces the prior distribution of the new estimated models (I-smoothing)

• MPE v.s. MMI– MMI treated the correct transcriptions as the numerator lattice and th

e whole word graph as the denominator lattice or the competing sequences

– MPE treats all possible correct sequences on the word graph as the numerator lattice, and treats all possible wrong sequences as the denominator lattice

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fMPE (cont.)

• Feature-space minimum phone error (fMPE) is a discriminative training method which adds an offset to the old feature

ttt Mhoy

current feature

transform matrix

high-dimensional feature

current frame

Each vector contains 10,000 Gaussian posterior probabilityAnd the Gaussian likelihoods are evaluated with no priors

average

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fMPE (cont.)

• Objective Function

using gradient descent to update the transformation matrix

Direct differential

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6

fMPE (cont.)

• When using only direct differential to update the transformation matrix, significant improvements are obtainable but then lost very soon when the acoustic model is retrained with ML

• The indirect differential part thus aims to reflect the model change from the ML training with new features,

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offset fMPE

• The difference of offset fMPE from the original fMPE is the definition of the high dimensional vector t h of posterior probabilities

where represents the posterior of i -th Gaussian at time tsize:

• The number of Gaussians needed is about 1000, which is significantly lower than 100000 for the original fMPE

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dimension dependent

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Dimension-weighted offset fMPE

• Different from the offset fMPE which gives the same weight on each dimension of the feature offset vector– calculates the posterior probability on each dimension of the feature

offset vector

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Experiments (on MATBN)

• Error rates (%) for MPE and fMPE for different features, on different acoustic levels.

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Experiments (cont.)

• CER(%) for offset fMPE and dimension-weighted offset fMPE with different features

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Connect to SPLICE

• Decomposition Scheme 1

= +

ty to M

th

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Connect to SPLICE (cont.)

• Compensation of the original feature is carried out by adding a large number of bias vectors, each of which is computed as a full-rank rotation of a small set of posterior probabilities

• Maximum-Likelihood estimation

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*i denotes the term greater than remaining (n-1) terms

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Connect to SPLICE (cont.)

• Decomposition Scheme 2

= +

ty to M

th

1p 1p qp

1q

1m

1h

2m 3m km

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14

Connect to SPLICE (cont.)

• The compensation vector consists of a linear weighted sum of a set of frame-independent correction vectors, where the weight is the posterior probability associated with the corresponding correction vector

• The key difference is– the bias vector for compensation in fMPE is specific to each time

frame t– the bias vector in feature-space stochastic matching is common

over all frames in the utterance