Tous droits réservés © 2005 CRIM The CRIM Systems for the NIST 2008 SRE Patrick Kenny, Najim...

Tous droits réservés © 2005 CRIM

The CRIM Systems for the The CRIM Systems for the NIST 2008 SRENIST 2008 SRE

Patrick Kenny, Najim Dehak and Pierre Ouellet

Centre de recherche informatique de Montreal (CRIM)


SystemsSystems• CRIM_2 was the primary system for all but

the core condition– Large stand-alone joint factor analysis (JFA)

system trained on pre-2006 data

• CRIM_1 was the primary system for the core condition– CRIM_1 = CRIM_2 + 3 other JFA systems

with different feature sets

• CRIM_3 = CRIM_2 + 2006 SRE data


OverviewOverview• Tasks involving multiple enrollment

recordings:– 8conv-short3, 3conv-short3

• Tasks involving 10 sec test recordings:– 10sec-10sec, short2-10sec, 8conv-10sec

• Najim Dehak will talk about– JFA with unconventional features– Post-eval experiments on the interview data

(following LPT and I4U)


Factor Analysis ConfigurationFactor Analysis Configuration

• 2K Gaussians, 60 dimensional features– 20 Gaussianized mfcc’s + first and second

derivatives

• 300 speaker factors

• 100 channel factors for telephone speech

• Additional 100 channel factors for microphone speech


Speaker VariabilitySpeaker Variability Prior distribution on speaker supervectors

s = m + vy + dz– m is the speaker-independent supervector– v is rectangular, low rank (eigenvectors)– d is diagonal– y, z standard Normal random vectors (speaker

factors)


Channel VariabilityChannel Variability Each supervector M is assumed to be a sum of a

speaker supervector and a channel supervector:

M = s + c

Prior distribution on channel supervectors

c = ux – u is rectangular, low rank (eigenchannels)– x standard Normal random


Enrollment: single utteranceEnrollment: single utterance The supervector for the utterance is

m + dz + vy + ux

Calculate the MAP estimates of x, y and z

The speaker supervector is

s + dz + vy

The full posterior distribution of s can be calculated in closed form (but this is messy unless d is 0)


Enrollment: 8conv caseEnrollment: 8conv case

Again the joint posterior distribution of the hidden variablescan be calculated in closed form.Unless d is 0, this is very messyTrick: pool the utterances together and ignore the fact that the x’s are different

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10 second test conditions10 second test conditions Many labs have reported difficulty in getting channel

factors or NAP to work under these conditions

The problem may be that it is unrealistic to attempt to produce point estimates (ML or MAP) of channel factors using 10 second test utterances

Probability rules say you should integrate over channel factors instead


Why is this not an issue for Why is this not an issue for long test utterances?long test utterances? If the test utterance is long, the posterior

distribution of the channel factors will be sharply peaked in the neighbourhood of the point estimate (MAP or ML).

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unless 0)|(

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Research ProblemResearch Problem How should factor analysis likelihoods and

posteriors be evaluated so as to take account of all of the relevant uncertainties?

- Uncertainty in the speaker factors

- Uncertainty in the channel factors

- Uncertainty in the assignment of observations to mixture components


Current SolutionCurrent Solution• Use point estimate of speaker factors

– Bayesian approach (using full posterior) doesn’t seem to help

• Integrate over the channel factors• Use the UBM to align frames with mixture

components– Tractable posterior + Jensen’s inequality gives lower

bound on likelihood (Niko Brummer) – Very fast if combined with LPT assumption

• Paradoxical results if speaker/channel dependent GMM’s used in place of UBM


Ideal Solution: Integrate over Ideal Solution: Integrate over all hidden variablesall hidden variables• Robbie Vogt (Odyssey 2004) did this for a

diagonal factor analysis model– No speaker or channel factors– Exact dynamic programming solution

• Variational Bayes offers an approximate solution in the general case– Assume that the posterior distribution factorizes into 3

terms (speaker factors, channel factors, assignments of frames to mixture components)

– Cycle through the factors to update them (like EM)– Jensen’s inequality gives lower bound on the

likelihood which increases on successive iterations


FusionFusion

• Fusing long term and short term features

• Pseudo-syllable unsupervised prosodic and MFCC’s contours segmentation.

• Six Legendre Polynomial coefficients for each contour.

• JFA without common factor (d=0)

• Logistic regression function (Focal).


Pseudo-syllable segmentationPseudo-syllable segmentation


Long term featuresLong term features

• Three long term systems:– 512 G, Features : Pitch + energy + duration

(13 dimension)– 1024 G, Features : 12 MFCCs contours +

energy + duration (79 dimension)– 1024 G, Features : 12 MFCCs contours +

pitch + energy + duration (85 dimension)


Short2-short3 : Tel-Tel det7Short2-short3 : Tel-Tel det7


Short2-short3 : Tel-Tel det8Short2-short3 : Tel-Tel det8


How to deal with interview How to deal with interview data?data?

• Interview eigenchannel trained on interview development data (as LPT and I4U).

• Small configuration of the Factor analayis– Features 20 Gaussianized MFCC’s + first derivatives– 300 speaker factors , d=0 (no common factor), 100

telephone channel factors.

• We carried out two experiments :– 50 TeL-Mic channel factors.– 50 TeL-Mic channel factors + 50 interview channel

factors.


NIST 2008 : Interview data –NIST 2008 : Interview data –det1det1


NIST 2008 : Interview data –NIST 2008 : Interview data –det1det1EER (%) MinDCF

Without interview eigenchannels

8.9% 0.0477389

Interview speaker utterances means

5.5% 0.0342164

Interview channel_2 utterance as means

5.7% 0.0360786

Interview & microphone

eigenchannels

5.7% 0.033472


ReferencesReferences

• A Study of Inter-Speaker Variability in Speaker Verification.

• Modeling prosodic features with joint factor analysis for speaker verification.

www.crim.ca/perso/patrick.kenny

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