Patent Application: US-201213567963-A

Abstract:
systems and methods for adjusting a discrete acoustic model complexity in an automatic speech recognition system . in some cases , the systems and methods include a discrete acoustic model , a pronunciation dictionary , and optionally a language model or a grammar model . in some cases , the methods include providing a speech database comprising multiple pairs , each pair including a speech recording called a waveform and an orthographic transcription of the waveform ; constructing the discrete acoustic model by converting the orthographic transcription into a phonetic transcription ; parameterizing the speech database by transforming the waveforms into a sequence of feature vectors and normalizing the sequences of the feature vectors ; and training the acoustic model with the normalized sequences of the feature vectors , wherein the complexity pi of the discrete acoustic model is further adjusted through a procedure that uses a given generalization coefficient n . other implementations are described .

Description:
choosing proper model complexity is a much studied topic in machine learning . however , there is no single procedure applicable for wide class of models . herein we restrict our attention to discrete models , a . k . a . histograms with data dependent partitions . the data dependent partition has both the cells shape and the granularity / resolution / complexity / number of the cells adjustable . the partition under consideration in this patent is derived from vector quantization [ 5 ] and it is thus the so called voronoi partition . the application of the invention is possible if there is a need for a classification based on training data , like e . g . in speakers recognition systems , recognition of faces , graphical signs and other types of data . a short account of vector quantization follows . our procedures for adjusting model complexity assumes the features are quantized [ 5 ]. there are several issues related to quantization of the features . one have to choose between lattice [ 6 ] and trained quantizers [ 7 ], between one - stage and product quantizers [ 5 ] etc . next , the quantizer resolution has to be decided upon . the quantizer resolution is given in case of lattice quantizers by volume of the cell and in case of trained quantizers by the number of codevectors in the codebook . since the features belong to the euclidean space of dimension p we talk here always of vector quantizers . vector quantizer can be viewed as a mapping from p dimensional euclidean space p onto a discrete set y ⊂ p , q : p → y where y ={ y 1 , . . . , y i }. set y is called codebook . elements of the codebook are the reproduction vectors or codevectors . vector quantizer tills the space into i sets known as quantizer bins or cells : defined as r i = q − 1 ( y i )={ xε p : q ( x )= y i }. the sets r i have a following property : it can be shown that the reproduction vector inside the partition element r i is optimal if it is a center of weight for that partition element . formally : where p ( x ) is the source distribution . once the source distribution is available implicitly by the training set , the ensemble averages are replaced by sample averages to compute actual placement of the reproduction vectors . the input vectors to the quantizer are assigned reproduction vectors according to the nearest neighbor rule . it can be shown that the nearest neighbor rule is optimal , minimizing distortion induced by the quantization . formally the nearest neighbor rule states : with any appropriate breaking of ties . partition defined according to ( 7 ) is called the voronoi partition . quantizer with bins ( countable but infinite number of them ), which are all the same and divide the whole space are known as lattice quantizers . the lattice quantizer , or more precisely the set of reproduction vectors , is defined as follows : where m is the so called generator matrix . volume of the lattice quantizer bin is given by : lattice quantizers do not require training but constructing them is a difficult mathematical task [ 8 ]. a fragment from a hexagonal lattice covering the whole plane is shown in fig4 . a different class of the quantizers is trained quantizers . there is a number of algorithms for obtaining a trained quantizer . to name a few , we have , the generalized lloyd algorithm ( gla ) [ 5 ], or a method by equitz [ 7 ], which requires less computations than the lloyd algorithm at the price of being less accurate ( this loss of accuracy is negligible in most practical applications ). an often applied workaround , which is aimed at lowering complexity of training and encoding is dividing the space ω of dimension dim ( ω )= p into subspaces ω = ω 1 × ω 2 such that dim ( ω )= dim ( ω 1 )+ dim ( ω 2 ). such quantizers are referred as product quantizers to . current practice regarding adjusting discrete model complexity is limited to a simple advice of using a codebook with e . g . 256 entries — this value is typically found in a number of sources dealing with speech recognition with the discrete models , cf . [ 9 ], [ 10 ]. this rather restrictive setting leaves no room for accurate modeling of phonetic densities especially if there are very large training sets available . the difference between a greedy ( low complexity ) model and an accurate ( high complexity ) model is illustrated in the fig5 . obviously the high complexity model from the fig5 requires more data to be trained reliably . however , the statement ‘ more data ’ is non - precise — there is no rule to set the partition optimally having the training set fixed . it would be also important to know , having a partition and an initial training set , what additional amount of training data is needed to have a proper model , regarding both accuracy and generalization . other questions of that kind are , having an initial sample how to obtain the total , approximate number of cells contained in the support of the phonetic density . such questions are answered by the following description of the invention . assumption of uniform distribution is restrictive . however , it gives important initial insight into the problem , and thus is briefly presented here . assume , that the probability density p ( x ) is of bounded support . next assume , that a space partition is given for which holds : ∫ r i p ( x ) dx = q , for all r i , such that r i ∩ s ≠ 0 / where s ={ x : p ( x )& gt ; 0 } is the mentioned support of the pdf p ( x ). next , let x ={ x 1 . . . x m } be a random sample , whose elements are quantized , that is each sample is attached a natural number in the range 1 , . . . , i . it could be seen , that such obtained indices of cells are governed by a multinomial distribution with k classes and k is less or equal i . it should be pointed out , that the number of cells k , which intersect with the support is unknown and our goal is to estimate it . let v will be a set of indices obtained by quantization of x . we can show , that conditional probability of the sample given the hypothetical k h is equal : where z is the number of distinct indices of bins included in v , s i is the number of repetitions of the bin with the index i , and m is the observation length . it could be seen that the maximum likelihood estimate for the hypothetical number of bins intersecting with the pdf under investigation , does not depend on the middle term , which includes the multinomial coefficient . thus the estimate can be obtained by : the likelihood ( 10 ) is equal zero for k b less than z . we can separate out the following three modi of this likelihood function : 1 ) the likelihood function is monotonically increasing in [ z ¥) 2 ) the likelihood function is monotonically decreasing in [ z ¥) 3 ) there is a single maximum in the range [ z ¥) it can be shown that the following conditions hold for each of the above listed modi : if m fulfills this condition then { circumflex over ( k )} h is equal z . one can prove the following , interesting from the theory viewpoint , property . this property establishes the link with known in the statistical literature problem of coupon collector [ 11 ]: in the above expression h ( k ) is the harmonic number equal , by definition , the expression in the numerator is the mean number of trials needed to learn all bins intersecting with the support , while the unknown number of such bins is k . the main vehicle of the proofs is the following expression valid for the harmonic numbers [ 12 ]: where c is the euler - mascheroni constant . it can be seen that asymptotically , as k approaches infinity , the terms after the logarithmic term vanish to zero . this leads to the following property : the proof for the condition 1 ) starts with taking logarithm of the considered expression ( eq . ( 11 )): suppose now that i a continuous variable , which setting follows from allowing that variable to take on non - integer values . it can be seen that the middle sum does not depend on k h so derivative w . r . t . that variable reads : the last expression allows us to state the condition 3 ) which is either : the loaner equation let us conclude that the sample length needed to learn a given percent of the bins intersecting with the support is a multiple of k . setting z = m we see that , indeed , this ( z = m ) is the sufficient and necessary condition for optimal k h approaching infinity , thus proving the condition 1 ). this is due to the following identity : it remains to prove the condition 2 ). in this case the maximum of the likelihood should be attained at k h = z . thus we have a following inequality : in fig6 , we illustrate the dependence of the data amount m needed to learn a given percent of bins in the support . next step will be derivation of the conditions analogous to the introduced in the previous section , which are distribution free ( we relax the assumption of bins of equal probabilities ). to achieve the desired effect we introduce the probabilities of bins p =[ p 1 , . . . , p k h ]. since we do not impose a constraint on the probabilities of bins the considered probability function is now in the form : where k ={ k 1 , . . . , k z }. we integrate the above function over a unit simplex d : note , that integrating out the probabilities in eq . ( 26 ) is not the only available strategy . another method would be to maximize over the joint vector of k h and p . as can be seen this is a polynomial optimization problem which is generally np - hard . however some approximation algorithms exist , which run in polynomial time , see e . g . [ 13 ]. another , a more viable one , approach would be to use the pmf estimator , with a proper handling of the back - off probabilities and use these estimated probabilities during computing a likelihood estimate of the joint vector according to ( 26 ). a good candidate algorithm for this approach could be the one given in [ 14 ]. in any case , as shown later in this document , the integrating - out strategy leads to neat mathematical results . maximization - strategy , though forms an interesting alternative to the natural laws of succession from [ 14 ], might be too computationally involved . let assume that all pmfs are equally likely . this corresponds to the assumption that we do not know the true pmf and attach to each possible p =[ p 1 , . . . , p k h ] an equal weight ( we assume they are equally probable ): where the equality ( 28 ) follows the fact , that the value of the integral does not depend on the choice and order of the probabilities in the monomial integrand . we present now the most important results without going into technical details . some details of the derivations are contained in the appendix . the following expression for probability of k h can be deduced starting from the equation ( 26 ): similarly to the previously studied case of equal probabilities of bins we can separate the following three modi : 1 . function is increasing for k h ≧ z if and only if m = z . 2 . function is decreasing for k h ≧ z if and only if m & gt ; z 2 . 3 . function has a single maximum at k h for k h ≧ z if and only if the fig7 shows how the data amount requirements change according to selected percentage of “ saturation ” of the support . by saturation we mean the percentage of the total number of bins having at least one training sample in it . in choosing quantizer complexity the idea is to balance the accuracy ( complexity of the model ) and the generalization ability of the model . the generalization ability is measured by the ratio of m and z , which we call the generalization coefficient in the remaining part of the patent . the larger the ratio is the better the model will generalize , what means it will work better for the samples outside the training set . however , as illustrated in the fig5 , the better generalizing model is the larger the cells are and the more ambiguities between classes arise . the ambiguity can be measured using the quantity known as the bayes risk . it can be derived that for a pair of classes , a and b , the optimal bayesian classifier [ 15 ] returns incorrectly the class label b while the observable comes from the class a actually , with the probability equal to the bayes risk . thus , formally speaking , the bayes risk is equal : in the section 0 devoted to computations of the sample needed to estimate the support ( entitled “ dependencies for the non - uniform distribution ”) we saw that the sample needed to learn as much as 99 % of the cells in the support is on the order of 100 × k . the question is if we actually need such a good generalization — coming inevitably at the price of lower accuracy . it seems that much of the cells learned with the generalization coefficient set to that number is of negligible low probability . the intuition is that we can discard such cells and increase the accuracy of the model sacrificing the generalization . the discarding of the cells does not increase significantly the bayes risk , since that cells are of such a low probability . as derived using monte - carlo experiments it suffices to take the generalization coefficient equal ˜ 8 to ‘ saturate ’ the bayes risk , what means that increasing the sample length beyond 8 × k , results in no further improvement of the classifier . this is a result of learning most of the ‘ typical ’ cells for the classes and discarding the low probability cells , which do not add to the bayes risk significantly . distribution of the number of codevectors in a resolution constrained product quantizers an element of the proposed invention is a method to distribute the codevectors of the resolution constrained , cf . [ 16 ], product vector quantizer between the parts of the product . the so called product codebook is given by c = c 1 × c 2 where the sum of the dimensions of the codevectors of c 1 and c 2 add up to give the dimension of the codevectors of c . the codevectors of the product codebook c are given in terms of the codevectors of c 1 and c 2 as : where y i εc , y i ( 1 ) εc 1 , y i ( 2 ) εc 2 and i = i 1 i 2 , i 1 =| c 1 |, i 2 =| c 2 |. in light of the above definition we propose the following procedure for choosing optimally the i 1 and i 2 to minimize total distortion . we start the derivation with recalling known from the high rate quantization theory results [ 16 ]. the distortion , assuming the so called gersho &# 39 ; s conjecture , introduced by a high rate , resolution constrained quantizer is equal : where g ( x ) is the density of the codevectors . the density of the codevectors is related to the number of such vectors by the following integral : according to the high rate quantization theory the optimal reproduction vectors density reads , in terms of the source distribution : where x lives in the product space ω = ω 1 × ω 2 and x ( 1 ) is the projection of the x onto the first subspace ω 1 , and x ( 2 ) is the projection of the x onto the second subspace ω 2 . the quantizers are embedded in the corresponding subspaces , thus we can write c 1 ⊂ ω 1 and c 2 ⊂ ω 2 . applying the high rate quantization theory results to the problem of distributing available i codevectors between the quantizers c 1 and c 2 we obtain the following lagrange equation for the distortion induced by the product quantizer : and λ is the lagrange multiplier . minimization of the lagrange [ 17 ] equation w . r . t . i 1 and i 2 and λ gives the desired solution ( this computation can be done with ease using any computer algebra system , thus we do not provide it here ) given above results the quantizer resolution selection proceeds as follows . let the complexity / resolution / number of codevectors / volume of the discrete model be denoted as π : let h be the number of resulting subphonetic units , typically there are three subphonetic units per triphone set m j = m and z j = 1 , jε { 1 , . . . , h }. train a quantizer using e . g . gla with i = π codevectors ( π represents the number of codevectors in case of a trained quantizer ), it could be possibly a product quantizer with number of codevectors i distributed among the part quantizers using the recipe from the section entitled “ distribution of the number of codevectors in a resolution constrained product quantizers ;” or , set the volume of a cell in a lattice quantizer to be half a way between maximal complexity ( minimal volume ) and minimal complexity ( maximal volume ) lattice quantizer find segmentation into subphonetic units — this step could be accomplished using e . g . viterbi training obtain m j and z j for each subphonetic unit , jε { 1 , . . . , h } if   min j ∈ { 1 , … , h }   ( m j  /  z j ) & lt ; n set π max = π ( or the volume of the cell of the lattice quantizer re - spectively ) else set π min = π ( or the volume of the cell of the lattice quantizer re - spectively ) end end the parameter n in this algorithm is the generalization coefficient introduced in section entitled “ choosing the sample length sufficient to ‘ saturate ’ the bayes risk .” the above algorithm should be performed for each stream of the features vectors , that is for the basic mfcc &# 39 ; s the delta mfcc &# 39 ; s and the delta - delta mfcc &# 39 ; s , separately ( cf . the section entitled “ computation and normalization of features ”). since the generalization coefficient may vary across triphone clusters , we take as the generalization coefficient the smallest one taken over all triphone clusters . to compute the generalization coefficient one need to go through the whole segmentation / training procedure . the segmentation / training procedure can be , e . g ., the viterbi training , see [ 2 ], page 142 . the algorithm results in optimal complexity quantizer given the training set . the returned optimal quantizer is a basis for forming the acoustic model in a straightforward manner , well known for those skilled in the art . the procedure for adjusting discrete model complexity can be executed during a training phase of a speech recognition system . necessary technical devices which allow for execution of the invented method are : any suitable computer with cpu / multiple cpus ( central processing unit ) with appropriate amount of ram ( random access memory ) and i / o ( input / output ) modules . for example it could be a desktop computer with a quad core intel i7 processor with 6 gb of ram , hard disk with 320 gb capacity , a keyboard , a mouse and a computer display . the procedure also can be parallelized for execution on a single server or a cluster of servers as well . it could be a server with two xeon 6 core processors , with 24 gb ram and 1tb hard disk . the latter configuration might be necessary if the training set grows especially large . the procedure for adjusting discrete model complexity has been carried out for a relatively small training set comprising 100 hours of speech data from around 100 different speakers consists of the following steps : preparation of the training set as described in the section entitled “ preliminary processing of the speech database .” the preparation of the speech database encompasses recording of acoustic waveforms using microphones , typically headsets or other , preferably electret or dynamic microphones . signals from the microphones are digitized with 22050 hz sampling rate and 16 bit per sample and stored in the mass memory . typically the signals are resampled to 16000 hz or 8000 hz depending on speech recognition application . the speech signals are accompanied with orthographic transcriptions stored as text files with e . g . utf - 8 encoding . in our example we used recordings of numerals sequences . using technical computer devices described above the invented method is executed . the method is provided in section entitled “ procedure for adjusting complexity .” the generalization coefficient n has been set to eight in our experiments . training of the acoustic model using , e . g ., baum - welch algorithm , see e . g . [ 18 ]. after these steps the acoustic model is ready for use in a speech recognition system , as shown in fig1 . asr system obtained using proposed invention is fast due to obtaining probability of a feature vector in a unit time . the operation of computing probability of a feature vector is a simple table lookup . simultaneously the system is more robust to speakers outside the training set than while using classical approach of creating acoustic model . such acoustic model optimized using proposed invention can be stored in memory of any device such as , for example , a mobile device , a laptop or a desktop device . the memory need not have very low access time , it could be even a slow flash memory . given appropriately large training set collected from a large number of speakers set the system obtained using proposed invention is truly speaker independent , and does not require adaptation . this is due to the introduced generalization coefficient and the introduced procedure for adjusting complexity of the discrete model . additionally , we observe an improvement in wer ( word error rate ) as compared to the classical system with the number of codevectors set arbitrarily without optimization . proposed method of adjusting complexity can be used virtually always if a fast and accurate classifiers are needed . examples include , but are not limited to : recognition , verification or authorization of speakers based on their voices , authorization based on a photography of a face , authorization based on fingerprints , recognition of digitized graphical signs such letters , musical scores etc . introduced dependencies allow also for estimation of the data amounts requirements needed to achieve assumed wer ( word error rate ) in a speech recognition system or other classifiers . the method leading to such operation is following , let n be equal eight : we gather initial set of training data . we assume a complexity pi1 and obtain acoustic model using data set length m1 which gives the generalization coefficient n . we assume a larger complexity pi2 and obtain acoustic model using data set length m2 , which gives the generalization coefficient n . we measure the wer for the systems created above and derive an extrapolation of wer for growing complexity . after obtaining complexity which leads to the satisfactory wer we compute , using introduced in this description dependencies , what m is needed to achieve such complexity at maintained generalization coefficient n . it can be shown using the brion &# 39 ; s formulae [ 19 ], that integral in eq . 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