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. Motivation. Phonetic transcription of DECEMBER. Gross errors. d ix CH eh m bcl b er.

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An Efficient Online Algorithm for Hierarchical Phoneme Classification

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An efficient online algorithm for hierarchical phoneme classification

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


Motivation

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

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Hierarchical classification

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

oy

aa

iy

sh

d

ow

ao

ih

s

k

uh

er

ey

th

p

uw

aw

eh

dh

t

ay

ae

zh

z

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Metric over phonetic tree

Metric Over Phonetic Tree

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

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Metric over phonetic tree1

b

a

Metric Over Phonetic Tree

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

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Metric over phonemes

b

a

Metric Over Phonemes

  • Metric semantics:γ(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

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Hierarchical classifier

W0

W1

W2

W3

W4

W5

W6

W7

W8

W9

W10

Hierarchical Classifier

  • Assume and

  • Associate a prototypewith each phoneme

  • Score of phonemeas

  • Classification rule:

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Hierarchical classifier1

w0

w1

w2

w3

w4

w5

w6

w7

w8

w9

w10

Hierarchical Classifier

  • Goal: maintain “close” to

  • Define

  • Goal: maintain small

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Online learning

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

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Tree loss

Tree Loss

  • Difficult to minimize directly

  • Instead upper bound bywherealso known as the hinge loss

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Online update

Local update – only nodesalong the path from to are updated

OnlineUpdate

w0

w1

w2

w3

w4

w5

w6

w7

w8

w9

w10

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Loss bound theorem

Loss BoundTheorem

  • sequence of examples

  • satisfies

  • Then

    where and

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Extension kernels

Extension: Kernels

  • Since

  • Note that

  • Therefore

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Experiments

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

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Experiments1

  • Greedy approach: solve a multiclass problem at nodes with at least 2 children

C

C

C

Experiments

  • Multiclass - Ignore the hierarchy

C

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Results

Results

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Results1

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

Syntheticdata

Phonemes

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Tree vs multiclass online learning

Tree vs. Multiclass Online Learning

  • Similarity between the prototypes in Multiclass and Tree training

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


Thanks

Thanks!

Large Margin Hierarchical Classification Joseph Keshet, The Hebrew University


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