Minimum Phoneme Error Based Heteroscedastic Linear Discriminant Analysis For Speech

RecognitionBing Zhang and Spyros Matsoukas,

BBN Technologies, 50 Moulton St. Cambridge

Reporter : Chang Chih Hao

Introduction

• LDA and HLDA– Better classification accuracy

– some common Limitations• None of them assumes any prior knowledge of confusable hypotheses

• Their objective functions do not directly relate to the word error rate (WER)

• Minimum Phoneme Error– Minimize phoneme errors in lattice-based training frameworks

– Since this criterion is closely related to WER, MPE_HLDA tends to be more robust than other projection methods, which makes it potentially better suited for a wider variety of features.

MPE Objection Function

• MPE-HLDA model

• MPE-HLDA aims at minimizing expected number of phoneme errors introduced by the MPE-HLDA model in a given hypothesis lattice, or equivalently maximizing the function

m m

Tm m

t t

A

C diag A A

o Ao

, | (4)

is the total number of training utterances,

is the sequence of p-dimensional observation vectors in utterance r,

is the "raw accuracy" score of wor

r

R

MPE r r rr w

r

r

F O P w O w

R

O

w

d hypothesis .rw

,m mC

MPE Objection Function

•

| is the posterior probability of hypothesis in the lattice

| |

|

is the language model probability of hypothesis ,

k : in order

r

r r r

k

r r r

r r k

r r rw

r r

P w O w

P O w P wP w O

P O w P w

P w w

to reduce acoustic scores dynamic range, thereby avoiding

the concentration of all posterior mass in the top-1 hypothesis of the lattice.

MPE Objection Function

• It can be shown that the derivative of (4) with respect to A is

, log | ,, (6)

, | ,

is the MPE score of utterance r (average accuracy over all hypotheses),

is the average accuracy ove

r

RMPE qr r

rr q

r r qr r

r

F O P O q rk D q r

A A

where

D q r P q O r q r

r

q

rr all hypotheses that contain arc q .

MPE Objection Function

•

•

log | , log | ,

and are the begin and end time of are ,

denotes the posterior probability of Gaussian m in arc at time t.

qr

qr

qr

r r

qr

Eqr r tm

t S m

q q r

mr

P O q r P o mt

A A

S E q

t q

1 1 1

1 1 1 1

log | ,t m mm m t p m m t

T T

m m t m t m m m p m m t m t m

Tmt t m t m

Tmt t m t m

P o mC C P I A C R

A

C C diag o o A C I A C o o

where

P diag o o

R o o

MPE Objection Function

• Therefore, Eq.(6) can be rewritten as

1 1

1

,

,

,

,

qr

r

r qr

qr

r

r qr

qr

r

r qr

MPE

m m m m p mm

Em

m r qr q t S

Em m

m r q tr q t S

Em m

m r q tm r q t S

F Ok C C g I A kJ

A

where

D q r t

g D q r t P

J C D q r t R

39*39

39*162

MPE-HLDA Implementation

• In theory, the derivative of the MPE-HLDA objective function can be computed based on Eq.(12), via s single forward-backward pass over the training lattices. In practice, however, it is not possible to fit all the full covariance matrices in memory.

• Two steps– First, run a forward-backward pass over the training lattices to acumulate

– Second, uses these statistics together with the full covariance matrices to synthesize the derivative.

• The Paper used gradient descent in updating the projection matrix.

MPE-HLDA Implementation

Experimental Framework

A Lp*n

n*l

l*1

p*1

Global feature projection

---there is more useful information in longer contexts

---Reduce the computational cost

Experimentation

• Conversational Telephone Speech (CTS)– 2300 hours of training data

• 800 hours : training the initial ML model

• 1500 hours : held-out training data – Lattice generation

– Discriminative training

– MPE-HLDA : only 370 hours

– Testing set• Eval03

• Dev04

Experimentation

• Conversational Telephone Speech (CTS)– Feature

• Frame concatenated PLP cepstra– 15 frames, l = 225, n = 130, p = 60

Experimentation

Experimentation

• Broadcast News (BN)– 600 hours : training the initial model (Hub4 and TDT)

– 330 hours : held-out data

Thanks