Abstract Gaussian-selection-based non-optimal search for speaker identification

Gaussian-selection-based non-optimal searchfor speaker identificationMarie Roch*San Diego State University,5500Campanile Drive,San Diego,CA 92182-7720,USA Received 3February 2004;received in revised form 28March 2005;accepted 5June 2005AbstractMost speaker identification systems train individual models for each speaker.This is done as individual models often yield better performance and they permit easier adaptation and enrollment.When classifying a speech token,the token is scored against each model and the maximum a priori decision rule is used to decide the classification label.Conse-quently,the cost of classification grows linearly for each token as the population size grows.When considering that the number of tokens to classify is also likely to grow linearly with the population,the total work load increases exponentially.This paper presents a preclassifier which generates an N -best hypothesis using a novel application of Gaussian selec-tion,and a transformation of the traditional tail test statistic which lets the implementer specify the tail region in terms of probability.The system is trained using parameters of individual speaker models and does not require the original feature vectors,even when enrolling new speakers or adapting existing ones.As the correct class label need only be in the N -best hypothesis set,it is possible to prune more Gaussians than in a traditional Gaussian selection application.The N -best hypothesis set is then evaluated using individual speaker models,resulting in an overall reduction of workload.Ó2005Elsevier B.V.All rights reserved.Keywords:Speaker recognition;Text-independent speaker identification;Talker recognition;Gaussian selection;Non-optimal search1.IntroductionTraditionally,speaker identification is imple-mented by training a single model for each speaker in the set of individuals to be identified.Identifica-tion is accomplished by scoring a test utterance against each model and using a decision rule,such as the maximum a posteriori (MAP)decision rule where the class of the highest scoring model is selected as the class label.The advantages of such schemes over training a single model with multiple class outputs is that enrollment of new speakers does not require the0167-6393/$-see front matter Ó2005Elsevier B.V.All rights reserved.doi:10.1016/j.specom.2005.06.003*Tel.:+16195945830;fax:+16195946746.E-mail address:marie.roch@Speech Communication xxx (2005)xxx–xxxtraining data for the existing speakers and the training of individual models is faster.The down-side to this approach is that the computational complexity required for identification grows line-arly for the classification of each speaker as the number of the speakers increases.Unless the majority of enrolled speakers are infrequent users of the system,it is reasonable to expect that as the number of registered users increase,the num-ber of classification requests could increase at least linearly.Under this assumption,the system load rises exponentially as the registered population in-creases due to the increase of requests and increase of models to check against.In this work,we develop a preclassifier which produces a hypothesis that a token is most likely to belong to one of a small subset of the possible classes.The token is then rescored against the tra-ditional per class models and afinal class label is assigned.The design goals are to produce a pre-classifier with the following properties:(1)The computational workload of the system isreduced.(2)Enrollment of new speakers should be of lowcost.Regeneration of the preclassifier as newspeakers are enrolled should not be cost pro-hibitive with respect to both time and spacerequirements.(3)There should be minimal or small impact onthe classification error e of the sys-tem should incur no more than a smallpenalty in classification performance.We will show that a system meeting the above criteria can be achieved through a novel applica-tion of Gaussian selection.A Gaussian selection system is constructed which evaluates a subset of the non-outlier Gaussians near each speaker.Un-like traditional Gaussian selection systems like those described in PichenyÕs(1999)review of large vocabulary dictation systems,there is no attempt to capture all of the distributions for which the point is not an outlier.A small subset of the distri-butions is sufficient to identify a set of promising candidates.This candidate set is then rescored using speaker-specific models and the MAP deci-sion rule is applied.It should be noted that the proposed system is non-optimal;there is no guarantee that the hypothesis set will contain the correct class of the token being classified.As will be demonstrated empirically in the experimental section,in most cases this has minimal impact on the classification error rate for the evaluated corpora.The remainder of this paper is organized as fol-lows:Section2describes an overview of existing techniques to reduce the computational load of speaker recognition systems.Next,we review Gaussian selection(Section3)and present a way to specify the outlier test in terms of probability. Section4describes how Gaussian selection can be applied to construct an efficient preclassifier which meets the stated design goals.Section5 describes the experimental methodology,and results are reported in Section6.Finally,we sum-marize ourfindings in Section7.2.BackgroundThe proposed Gaussian-selection-based preclas-sifier differs from other non-optimal search tech-niques such as the well-known beam search (Huang et al.,2001),time-reordered beam search of Pellom and Hansen(1998),and confidence-based pruning(Kinnunen et al.,in press)in that classification speed can be increased without prun-ing candidates before all feature vectors are consid-ered,but the system could of course be combined with such techniques.In terms of system architec-ture,the proposed technique is similar to the two stage classification system of Pan et al.(2000)where two learning vector quantizers(LVQ)of differing size are used forfirst and second pass scoring.There are several partition-based approaches that have been proposed for speech and speaker recognition systems.The partitioning results in a pruning of Gaussian evaluations.These systems can be separated into techniques which provide separate partitions for each model and those that partition the entire feature space.Pruning of Gaussians in these techniques occurs when com-puting the posterior likelihood for thefinal classi-fication decision,and in all cases it is not part of a N-best match strategy.2M.Roch/Speech Communication xxx(2005)xxx–xxxModel-specific partitioning schemes include the original Gaussian selection scheme of Bocchieri (1993)(which is discussed in the next section)as well as proposals by Lin et al.(1996),and Auc-kenthaler and Mason(2001).LVQ has been used to partition the feature space for speaker identifi-cation by Lin et al.(1996)with each partition rep-resented by a Gaussian mixture model(GMM). Auckenthaler and Mason(2001)applied Gaussian selection to the speaker verification task.They also developed so-called‘‘hash models,’’where mix-tures of a low-order GMM contained mappings indicating which mixtures of a larger GMM should be evaluated.Examples of feature space partitioning can be found in(Reynolds et al.,2000;Padmanabhan et al.,1999;Xiang and Berger,2003).In a speaker verification task,Reynolds et al.(2000)construct a universal background model(UBM)for speaker verification which is a GMM consisting of speech from a large set of disjoint speakers.Individual GMM speaker models are adapted from the UBM using maximum a posteriori(MAP)adapta-tion of the mixture means.When scoring,the UBM is scoredfirst and the mixtures of the adapted GMM corresponding to the top-ranking UBM mixtures are subsequently scored.Padmanabhan et al.(1999)proposed the parti-tioning of the feature space through the use of decision trees in a speech recognition task.During classification,the decision tree is traversed for each feature vector,and only classes associated with the leaf node are evaluated.As the feature data is re-quired for creating the decision tree,this technique would require that training data be retained mak-ing it difficult to meet design goal2in Section1 when new speakers are enrolled or existing ones are adapted.Davenport et al.(1999)have pro-posed a simpler version of this scheme for the BBN Byblos system.Xiang and Berger(2003)created a tree struc-tured classification system for speaker verification. The tree structure was based on the work of Shi-noda and Lee(2001).Each split point forms an interior node of a tree which they call a structural background model(SBM).Efficient computation is achieved by scoring each child of the root and only scoring the children of the best mixture.This technique is applied recursively until the leaf nodes are reached.This results in efficient scoring with a slight increase in error rate,similar to that of Gaussian selection techniques.The error rate is re-duced by exploiting the multiple resolutions of the model,using a multi-layer perceptron trained by back-propagation.The authors propose that the system could be extended to speaker identification by adding one output node per class to the neural network.The training time and training data stor-age requirements would make the neural network portion of this model difficult to apply to speaker identification in situations where new enrollment or adaptation is a common occurrence.The proposed preclassifier falls in the category of feature space partitioning methods and differs from the aforementioned techniques although it is possible to combine it with some of the existing techniques as will be briefly discussed in the conclusion.3.Gaussian selectionThe evaluation of probability density functions (pdfs)in parametric statistical models is a compu-tationally expensive task.For any given observa-tion,the observation is likely to be an outlier with respect to many of the modelsÕdensity func-tions.The goal of Gaussian selection is to identify Gaussians where the observation is an outlier and replace their evaluation with a small constant or table lookup.Bocchieri(1993)was thefirst to propose a tech-nique to efficiently partition a set of distributions into outlier versus non-outlier distributions and to use this knowledge to reduce the set of pdfs that need be evaluated.In his algorithm,the feature space is partitioned by a vector quantization (VQ)codebook which is generated from the means of the Gaussian distributions of an HMM.Each of the codewords is examined to determine whether or not it would be considered an outlier with respect to all of the pdfs in the model.The pdfs for which the codeword is not an outlier are retained as a set which later researchers called a short list.The same pdf may appear on multiple short lists.M.Roch/Speech Communication xxx(2005)xxx–xxx3During recognition,observed feature vectors are quantized to the nearest codeword and the pdfs on the short list are evaluated.The contribution of the omitted pdfs is represented by the addition of a small constant.For a more detailed introduction to Gaussian selection,the interested reader is referred to Gales et al.(1999)whose presentation we follow where possible.For brevity,we only analyze GMMs,but the discussion is applicable to HMMs with minor changes.Before giving a formal introduction to Gauss-ian selection,we will introduce some useful nota-tion for GMMs and VQ Codebooks.It is assumed that the reader is familiar with these con-cepts;details can be found in standard texts such as Huang et al.(2001).Let us assume that a GMM is denoted as a 4-tu-ple M =(a ,l ,R ,h )of N m mixtures where each mix-ture 16j 6N m is a normal distribution N ðl j ;R j Þwith prior weight a j such that P N mj ¼1a j ¼1.It is as-sumed that the variance–covariance matrices R are diagonal.After an appropriate initial guess,the weights can be estimated by the expectation maxi-mization algorithm.The term h denotes the N h -dimensional feature space R N h .A VQ codebook is denoted as a 4-tuple V =(/,d ,q ,h )where:/is a set of N /codewords f /1;/2;...;/N /g &h ;d :h Âh !R is a distance metric which measures the distortion between two vectors.A common definition of d is the Euclidean distortion,or squared distance metric.q :h !/is a function which maps a vector x 2h to the minimum distortion codeword:q ðx Þ¼arg min /i 2/d ð/i ;x Þ.h is the N h -dimensional fea-ture space domain.In cases where the vectors of h being quantized are means of Gaussians them-selves,other distortion metrics such as the sym-metric Kullback–Leibler divergence have been used (e.g.Shinoda and Lee,2001).A codebook V is trained from the means of a specific GMM M .Next,each codeword /j is com-pared with the set of GMM mixtures to determine whether or not the codeword is an outlier with re-spect to individual mixtures.The test originally proposed for Gaussian selection by Bocchieri (1993)to determine if the m th Gaussian is an out-lier is shown in (1):outlier ðm ;/j Þ¼11N h P N h i ¼1ð/j ði ÞÀl m ði ÞÞ2R m ði ;i Þ>H ;1N hP N h i ¼1ð/j ði ÞÀl m ði ÞÞ2R m ði ;i Þ6H ;8>>><>>>:ð1Þwhere H is empirically determined and signifi-cantly greater than 1.In Bocchieri Õs study,he examined values between 1.5and 4.0.By analyzing (1),we can write a different repre-sentation of the tail test which provides better in-sight into the outlier identification process.Letus define z i ¼/j ði ÞÀl m ði ÞffiffiffiffiffiffiffiffiffiffiR m ði ;i Þp.As the codewords /j are representative of observations drawn from a nor-mal distribution and the components are assumedto be independent,each z i is representative of inde-pendent and identically distributed vectors with a distribution N ð0;1Þ.Consequently,(1)can be thought of as a scaled sum of squared z scores.The sum of N h independent and identically distrib-uted squared samples from a standard normal dis-tribution has a chi-squared distribution with N h degrees of freedom (Hogg and Allen,1978)which we will denote as v 2(N h ).Thus,(1)may be rewrit-ten asoutlier ðB s ;m ;/j Þ¼1P N h i ¼1z 2i >H 0;0P N h i ¼1z 2i 6H 0;8>>><>>>:ð2Þwhere H 0=N h H .The Pr P N h i ¼1z 2i ÀÁ6H 0can be found by using the cumulative distribution func-tion (cdf)for v 2(N h )which we will denote with operator F .In Bocchieri Õs study,he used 38dimen-sional feature vectors.When H =1.5,it corre-sponds to rejecting points as outliers if they lie within the tail 2.45%of the distribution (1ÀF (38·1.5)).By using the inverse cumulative distribution function F À1,it is possible to specify a probability which indicates what portion q of the distribution should be considered the tail:outlier ðB s ;m ;/j Þ¼1P N h i ¼1z 2i >F À1ð1Àq Þ;0P N h i ¼1z 2i 6FÀ1ð1Àq Þ.8>>><>>>:ð3Þ4M.Roch /Speech Communication xxx (2005)xxx–xxxAs an example,to specify that points lying on the last5%of the tails should be considered outliers, one could compute FÀ1(.95)=53.384,or a value of H=1.405in Eq.(1).It is worth mentioning that v2(N h)is well approximated by NðN h;2N hÞfor large enough N h and that the inverse cdf of the normal distribution could also be used.Unlike Eq.(1),Eq.(3)permits implementers to specify outlier detection in a manner invariant to the dimensionality of the space.The robust estimation of variances is frequently a problem for GMMs,and when this is the case both Bocchieri and Gales et al.propose alterna-tives for the mixture specific variance term.Boc-chieri(1993)suggested using the mean of all variances and Gales et al.(1999)suggested using the geometric mean of the mixture variance and the mean of the variances.Throughout this work, we will use GalesÕs variance estimate unless other-wise noted.Once an appropriate tail region has been speci-fied,each codeword/j is examined to determine whether or not it is an outlier with respect to each of the mixtures.The mixtures for which/j is not an outlier are retained in a short list which we denote SL j.During classification,each observation o t is quantized to/j and the Gaussians in SL j are eval-uated with respect to o t.A small constant value is added to represent the missing probability from the distributions for which the observation is an outlier.The constant can be set globally,or on a per codeword basis.Error rates for speech recogni-tion tasks using Gaussian selection with HMMs show little degradation when compared to the evaluation of all Gaussians,and there are still sig-nificant savings in the number of operations in the presence of the VQ overhead(Bocchieri,1993; Gales et al.,1999).4.An N-best preclassifierGiven a token which consists of a set of obser-vations from a speaker:O={o1,o2,...,o T},the goal of a speaker identification classifier is to choose the class label C O which corresponds to the person who generated O.If a preclassifier can efficiently and successfully determine a hypothesis H N¼f C h1;C h2;...;C hNg where C O2H N and j H N j is smaller than the total number of classes N C,the work of the classifier can be reduced.Fig.1provides an overview of the system. Acoustic feature vectors are quantized to a code-word in a global codebook that is created by clus-tering the means of the GMMs themselves.Each codeword has a Gaussian short list associated with it which may contain Gaussians from multiple models.The lengths of the short lists are influ-enced by the percentage of the Gaussians labeled as tails by q.As q increases,the short list size de-creases,possibly at the expense of accuracy.This provides a time versus accuracy performance trade offfamiliar to implementers of Gaussian selection. As the short list size decreases,small differences in the probability may be enough to change the deci-sion from the correct class to an incorrect one.In a standard Gaussian selection implementation,one would need to increase the threshold once this behavior began to occur.By using an N-best preclassifier,as long as the correct class is ranked in the highest NlikelihoodFig.1.Two stage classification.Vectors are quantized to a codebook trained from the means of GMMs.Shortlists associated with each codeword identify relevant pdfs to evaluate.The highest ranking speakers are classified in a second stage.The preclassifier is shown separately Fig.2.M.Roch/Speech Communication xxx(2005)xxx–xxx5scores,the second stage can provide a more thor-ough analysis and the final decision may indeed be the correct class.The second stage permits the first stage to aggressively set q to values that would otherwise lead to unacceptable performance.Like any preclassifier,the work done in the first stage must be significantly less than evaluating the com-plete set if the goal is to reduce computation time.First stage classification begins by quantizing each input vector to the nearest codeword (Fig.2).Then for each model,the likelihood of the input vector o t is computed given the Gaussi-ans on the short lists.The small probability due to the mixtures for which o t lies on their tails is approximated by the likelihood of the codeword given the culled mixtures.This value is precom-puted and is retrieved by table lookup during rec-ognition.The likelihoods for each observation are merged on a per class basis in the standard way,(e.g.log sum)and then ranked to determine the N -best set.The worst case complexity of the preclassifier is determined by the cost of quantization,q (o t )!/j ,evaluation of the Gaussians from the correspond-ing short list SL j ,and the sorting of a statistic of the T likelihoods.Codeword lookup of a single vector can be performed in O ðN /N h Þassuming a Euclidean dis-tortion function.With the assumption of indepen-dent components,each pdf on the short list can be evaluated in O ðN h Þtime.Thus,in a worst case sce-nario,the time cost is O ðT ðN /N h þN h j SL max jÞÞper token where j SL max j denotes the maximum num-ber of Gaussians irrespective of class to appear in the short lists.In addition,a small time cost is incurred for sorting the statistic of the scores.As this is negligible in comparison to the rest of the operation we will omit it in our analysis.Based upon our assumption in Section 1that the classification requests grow proportionally to the population size,the preclassification cost for a set of tokens is:O ðN c T ½N /N h þj SL max j N h Þ.ð4ÞThe cost of classification is the cost of the hypoth-esis set plus full evaluation of the j H N j models in the N best speaker set:O ðN c T ½N h ðN /þj SL max jÞ þN c TN h N m j H N jÞð5Þ¼O ðN c TN h ½N /þj SL max j þN m j H N j Þ.ð6ÞThis is in contrast to the cost of complete evalua-tion which is similar to the cost of the second stage (right most term of (5))except that j H N j is replaced with N C as all models must be evaluated:O ðN 2c TN m N h Þ.ð7ÞReduction in workload can be achieved when j H N j (N c and j SL max j (N c N m .When new speakers enroll,the K means cluster-ing algorithm must be rerun and new short lists created.Ignoring the cost of computing the distor-tion between the codewords and the means of the Gaussians,K means has a complexity of O ðIN /N c N m Þwhere I is the number of iterations.Thus the growth of clustering cost is linear with respect to population size.Determining the short lists also has a complexity that grows linearly.Each time a new speaker is enrolled,there will be an additional N /·N c outlier tests to perform.In practice the preclassifier can be trained in a matter of minutes even with large problemsets.Fig.2.First stage.Appropriate short list set is identified by VQ codeword /j and short lists are evaluated for the original observation.For many models,the short lists will be empty.Culled Gaussians are approximated by a table lookup.6M.Roch /Speech Communication xxx (2005)xxx–xxx5.Experimental methodologyTwo corpora were selected to illustrate a variety of different test conditions and population sizes. To illustrate the effectiveness of the preclassifier, it was considered desirable to test under situations where the baseline GMM system could achieve low error rates as well as situations where the error rate was higher.For this reason,the TIMIT and the1999NIST Speaker Recognition corpora were selected for this study.TIMIT(Garofolo et al.,1993)contains record-ings of192female and438male subjects speaking phonetically diverse material under ideal condi-tions.Each speaker has10short sentences col-lected from a speaker in a single session.The sentences can be categorized into three groups. The‘‘sx’’sentences provide coverage of the pho-netic space,the‘‘sa’’sentences are intended to show dialectical variation,and the‘‘si’’sentences contain varied phones.Thefirst8utterances (approximately24s)are used for training and the last two‘‘sx’’phrases form separate3s tests. The conditions of this corpus permit high accuracy.The NIST1999Speaker Recognition Evalua-tion(Martin and Przybocki,2000)is a subset of the Switchboard2Phase3corpus which contains telephone conversations between speakers primar-ily from the the southern United States.The callers were encouraged to use multiple handsets,and the directory number is usually used to infer matched/ unmatched conditions.The corpus is designed pri-marily for speaker detection and tracking tasks, and the study by Kinnunen et al.(in press)is the only study of speaker identification using this cor-pus of which the author is aware.Kinnunen et al. limited themselves to a matched channel condition study using the male speakers.There are207 speakers whofit this criterion.Each speaker has anywhere from1to8test tokens from matching directory numbers for a total of692test tokens. We use the same test plan as Kinnunen et al.in or-der to be able to compare results,but also add the 287matched channel female speakers(997test to-kens)as a separate evaluation task.Throughout the remainder of this work,we will refer to this corpus as the NIST corpus.Features are extracted from the speech by fram-ing the data into25ms windows advanced every 10ms.A Hamming window is applied to each frame before Mel cepstral analysis using24filters. For both corpora,24Melfilters cover a telephone speech bandwidth of200–3500Hz(Rey,1983). Thefirst20Melfiltered cepstral coefficients (MFCC)plus MFCC0are extracted from the log Melfilterbanks by a discrete cosine transform. The NIST data is further processed:the mean of each token is subtracted and the the token is end-pointed.Speech activity is detected by training a2 mixture GMM on MFCC0(three iterations of the EM algorithm)and solving for the Bayes decision boundary.Frames with MFCC0above the deci-sion threshold are retained.MFCC0is discarded before training and testing.With the exception of endpointing,feature extraction was done as a pre-processing step using HTK(Young et al.,2002). The recognizer was implemented in a combination of C and Matlab,and experiments were performed on reasonably unloaded dual Opteron242ma-chines running the Linux2.6kernel.During enrollment,32mixture GMMs are trained for the TIMIT speakers.The NIST speak-ers are modeled in two ways.Speakers were either represented as64mixture GMMs or as models adapted from a universal background model (UBM).Training data for the UBMs came from the Speaker Identification Research(SPIDRE) corpus(Martin et al.,1994),a subset of Switch-board I with similar characteristics to the NIST data.One token from each of the18female and 27male‘‘target speakers’’was used to train gender specific UBMs with1024mixtures.Maximum a posteriori adaptation as described by Reynolds et al.(2000)was used to create speaker specific mean adapted models from the UBMs using the NIST training data.The64mixture speaker spe-cific models and UBMs were initialized with the LBG binary splitting algorithm(Linde et al., 1980)and refined with10iterations of the expecta-tion maximization algorithm.MAP adaptation was not used for the TIMIT corpus due to the excellent classification rate with the32mixture GMMs.When scoring the UBM derived models,we used ReynoldsÕheuristic which scores all mixtures of the UBMfirst,then onlyM.Roch/Speech Communication xxx(2005)xxx–xxx7scores the corresponding highest5mixtures in the adapted models.The baseline results are summarized in Table1 and are comparable to that of other studies using the same corpora(Reynolds,1995;Kinnunen et al.,in press).Confidence intervals for the error rates are estimated using the normal test approxi-mation for binomials(Huang et al.,2001).The TI-MIT classification error rate is 1.6%for the females and0%for the males.In contrast,the male telephone NIST error rates are in the14%range with an approximate6%absolute reduction in er-ror rate when the speaker models are adapted from UBMs.The female NIST speakers,a population that was nearly40%larger,had significantly high-er error rates.As with the male data,the UBMs outperformed the models trained without the ben-efit of prior information even though the amount of prior training information was limited.Analysis of the female UBM results showed that about40% of the error could be attributed to misclassifying tokens as one of15speakers(the‘‘wolves’’).The author is not aware of any published speaker iden-tification studies on this data set.Codebook training for the preclassifier was accomplished using the same procedure used to initialize the GMMs.Experiments not reported here used the Kullback–Leibler symmetric dis-tance as the distortion metric for the VQ.This did not result in significant performance differ-ences,so the simpler Euclidean distortion metric is used throughout.When determining whether or not points in a VQ partition are outliers,the geometric mean variance weighting scheme(Gales et al.,1999)was used to compute the z scores in Eq.(3)for all GMMs except for the adapted means models as the variance estimates from the UBMS tend to be more robust.6.ResultsInsight into the behavior of the preclassifier can be seen by examining the N-best hypothesis sets. The tunable parameters which affect the perfor-mance of the algorithm are the size of the codebook,the percentage of each Gaussian distri-bution for which points are defined as outliers(q), and the size of the hypothesis set H N.Experiments not reported here on TIMIT and NTIMIT(tele-phone version of TIMIT)indicated mild sensitivity to codebook size,and we selected a1024word codebook.Fig.3shows a typical N-best error rate for varying values of q.To be effective,the preclassi-fier must produce an N-best error rate which is as good or better than the second stage classifier. In practice,having the same error rate as the sec-ond stage is insufficient.The preclassifier learns a different set of decision boundaries than the sec-ond stage.Once a correct class is pruned fromTable1Speaker identification error rates and their95%confidence intervals on corpora without preclassificationCorpus Mixtures Pop.size ErrorRate95%CI TIMIT female321920.016±0.0125 TIMIT male324380.000NA NIST1999male642070.198±0.030 NIST1999male(UBM)10242070.142±0.026 NIST1999female642870.486±0.031NIST1999 female(UBM)10242870.382±0.153Fig. 3.N-best error rate for males on a matched handsetspeaker identification task using64mixture GMMs and thematched handset male speakers in the NIST1999SpeakerRecognition Corpus.Error rate is a function of the probabilitythreshold q which determines which codewords are outliers foreach mixture and the size of the N-best hypothesis.The baselineerror rate is shown as a solid horizontal line with the dotted95%confidence interval lines above and below.8M.Roch/Speech Communication xxx(2005)xxx–xxx。