An Efficient Online Algorithm for Hierarchical Phoneme Classification

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An Efficient Online Algorithm for Hierarchical
Phoneme Classification

• Joseph Keshet
• joint work with Ofer Dekel and Yoram Singer
• The Hebrew University, Israel

MLMI 04 Martigny, Switzerland
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Motivation
Phonetic transcription of DECEMBER
Gross errors
d ix CH eh m bcl b er
Minor errors
d AE s eh m bcl b er
d ix s eh NASAL bcl b er
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Hierarchical Classification

• Goal spoken phoneme recognition

PHONEMES
Sononorants
Silences
Nasals
Obstruents
Liquids
n
m
ng
l
Vowels
y
w
Affricates
r
Plosives
jh
Fricatives
ch
Front
Center
Back
f
b
v
g
sh
oy
aa
iy
d
s
ow
ao
ih
k
th
uh
er
ey
p
dh
uw
aw
eh
t
zh
ay
ae
z
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Metric Over Phonetic Tree

• A given hierarchy induces a metric over the set
  of phonemes ? tree distance

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Metric Over Phonetic Tree

• A given hierarchy induces a metric over the set
  of phonemes ? tree distance

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Metric Over Phonemes

• Metric semantics?(a,b) is the severity of
  predicting phoneme group b instead of correct
  phoneme a

• Our high-level goal
• Tolerate minor errors
• Sibling errors
• Under-confident predictions - predicting a parent
• but, avoid major errors

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Hierarchical Classifier

• Assume and
• Associate a prototypewith each phoneme
• Score of phonemeas
• Classification rule

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Hierarchical Classifier

• Goal maintain close to
• Define
• Goal maintain small

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Online Learning

• For
• Receive an acoustic vector
• Predict a phoneme
• Receive correct phoneme
• Suffer tree-based penalty
• Apply update rule to obtain

Goal Suffer a small cumulative tree error
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Tree Loss

• Difficult to minimize
  directly
• Instead upper bound by
  wherealso known as the hinge loss

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Online Update
w0
w1
w2
w6
w7
w4
w5
w8
w3
w10
w9
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Loss Bound Theorem

• sequence of examples
• satisfies
• Then
• where and

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Extension Kernels

• Since
• Note that
• Therefore

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Experiments

• Synthetic data
• Symmetric tree of depth 4, fan out 3, 121 labels
• Prototypes orthogonal set in with
  Gaussian noise
• 100 train instances and 50 test instances per
  label
• Phoneme recognition
• Subset of the TIMIT corpus
• 55 phonemes and phoneme groups
• MFCC??? front-end, concatenation of 5 frames
• RBF kernel
• 2000 train vectors and 500 test vector per phoneme

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Experiments

• Multiclass - Ignore the hierarchy

C
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Results
  Averaged Tree Error Multiclass Error
Synthetic data (tree) 0.05 5
Synthetic data (multiclass) 0.11 8.6
Synthetic data (greedy) 0.52 34.9
Phonemes (tree) 1.3 40.6
Phonemes (multiclass) 1.41 41.8
Phonemes (greedy) 2.48 58.2
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Results
Difference between the tree error rates of the
tree algorithm and the multiclass (MC) algorithm
gross errors
Tree err-MC err
Tree err-MC err
minor errors
Synthetic data
Phonemes
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Tree vs. Multiclass Online Learning

• Similarity between the prototypes in Multiclass
  and Tree training

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Thanks!