Tous droits réservés © 2005 CRIM The CRIM Systems for the NIST 2008 SRE Patrick Kenny, Najim Dehak and Pierre Ouellet Centre de recherche informatique de Montreal (CRIM)

Tous droits réservés © 2005 CRIM Systems 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_ SRE data

Tous droits réservés © 2005 CRIM Overview 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)

Tous droits réservés © 2005 CRIM Factor 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

Tous droits réservés © 2005 CRIM Speaker 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)

Tous droits réservés © 2005 CRIM Channel 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

Tous droits réservés © 2005 CRIM Enrollment: 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)

Tous droits réservés © 2005 CRIM Enrollment: 8conv case Again the joint posterior distribution of the hidden variables can be calculated in closed form. Unless d is 0, this is very messy Trick: pool the utterances together and ignore the fact that the x’s are different

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10 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

Tous droits réservés © 2005 CRIM Why is this not an issue for 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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Research 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

Tous droits réservés © 2005 CRIM Current 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

Tous droits réservés © 2005 CRIM Ideal Solution: Integrate over all 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

Tous droits réservés © 2005 CRIM Fusion 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).

Tous droits réservés © 2005 CRIM Pseudo-syllable segmentation

Tous droits réservés © 2005 CRIM Long 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)

Tous droits réservés © 2005 CRIM Short2-short3 : Tel-Tel det7

Tous droits réservés © 2005 CRIM Short2-short3 : Tel-Tel det8

Tous droits réservés © 2005 CRIM How to deal with interview 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.

Tous droits réservés © 2005 CRIM NIST 2008 : Interview data – det1

Tous droits réservés © 2005 CRIM NIST 2008 : Interview data – det1 EER (%)MinDCF Without interview eigenchannels 8.9% Interview speaker utterances means 5.5% Interview channel_2 utterance as means 5.7% Interview & microphone eigenchannels 5.7%

Tous droits réservés © 2005 CRIM References A Study of Inter-Speaker Variability in Speaker Verification. Modeling prosodic features with joint factor analysis for speaker verification.