Sausage

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Sausage

• Lidia Mangu
• Eric Brill
• Andreas Stolcke
• Presenter Jen-Wei Kuo
• 2004/ 9 /24

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Referred Reference

• CSL00 Finding Consensus in Speech Recognition
  Word Error Minimization and other Applications of
  Confusion Networks
• Eurospeech99 Finding Consensus among Words
  Lattice-Based Word Error Minimization
• Eurospeech97 Explicit Word Error Minimization in
  N-Best List Rescoring

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Motivation

• The mismatch between the standard scoring
  paradigm (MAP) and the evaluation metric (WER).

maximize sentence posterior probability ?
minimize sentence level error
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An Example
Correct answer IM DOING FINE
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Word Error Minimization

• Minimizing the expected word error under the
  posterior distribution

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N-best Approximation
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Lattice-Based Word Error Minimization

• Computational Problem
• Several orders of magnitude larger than in N-best
  lists of practical size.
• No efficient algorithm of this kind.
• Fundamental Difficulty
• Objective function is based on pairwise string
  distance, a nonlocal measure.
• Solution
• Replace pairwise string alignment with a modified
  multiple string alignment.
• WE (word error) ? MWE (modified word error)

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Lattice to Confusion Network
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Multiple Alignment

• Finding the optimal alignment is a problem for
  which no efficient solution is known (Gusfield,
  1992)
• We resort to a heuristic approach based on
  lattice topology.

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Algorithms

• Step1. Arc Pruning
• Step2. Same-Arc Clustering
• Step3. Intra-Word Clustering
• Step4. Same-Phones Clustering
• Step5. Inter-Word Clustering
• Step6. Adding null hypothesis
• Step7. Consensus-based Lattice Pruning

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Arc Pruning
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Intra-Word Clustering

• Same-Arc Clustering
• Arcs with with same word_id, start frame and end
  frame would be merged first.
• Intra-Word Clustering
• Arcs with same word_id would be merged.

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Same-Phones Clustering

• Same-Phones Clustering
• Arcs with same phone sequences would be clustered
  in this stage.

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Inter-Word Clustering

• Inter-Word Clustering
• Remaining arcs be clustered at this stage
  finally.

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Adding null hypothesis

• For each equivalent class, if the sum of the
  posterior probabilities is less than threshold
  (0.6) than add the null hypothesis to the class.

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Consensus-based Lattice Pruning

• Standard Method ? Likelihood-based
• Paths whose overall score differs by more than a
  threshold from the best-scoring path are removed
  from the word graph.
• Proposed Method ? Consensus-based
• Firstly we construct a pruned confusion network.
• Then intersect the original lattice with the
  pruned confusion network.

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Algorithm
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An Example

• How to merge ?

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?
?
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Computational Issues

• Partial Order ?Stupid Method
• History-based Look-ahead
• Apply first-pass search to find the history arcs
  for each arc. ? Generate the initial partial
  ordering.
• While clusters are merged, lots of computation
  for (recursive) updates are needed.
• Thousands of arcs ? need lots of memory storage.

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Computational Issues An example
C?A
If we merge B and C, what happened?
J?A
D?A
K?A
A
B
M?A
F?A
C
D
F
G?A
A
L?A
N?A
E
G
J
H
L
N
I
K
M
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Experimental Set-up

• Lattices was built using HTK
• Training Corpus
• Trained with about 60 hours of Switchboard
  speech.
• LM is a backoff trigram model trained on 2.2
  million words of Switchboard transcripts.
• Testing Corpus
• Test set in the 1997 JHU

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Experimental Results
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Experimental Results
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Confusion Network Analyses
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Other Approaches

• ROVER (Recognizer Output Voting Error Reduction)