Adjusting a deep neural network acoustic model

A computer-implemented method according to one embodiment includes estimating a speaker dependent acoustic model utilizing test speech data and a hybrid estimation technique, transforming labeled speech data to create transformed speech data, utilizing the speaker dependent acoustic model and a nonlinear transformation, and adjusting a deep neural network (DNN) acoustic model, utilizing the transformed speech data.

BACKGROUND

The present invention relates to automatic speech recognition (ASR), and more specifically, this invention relates to adjusting a deep neural network (DNN) acoustic model used in ASR.

Deep neural network (DNN) acoustic models are frequently used in the performance of automatic speech recognition (ASR). However, current methodologies for adapting DNN acoustic models to new test conditions suffer from covariate shift which arises from a distribution mismatch between training data and test data.

SUMMARY

A computer-implemented method according to one embodiment includes estimating a speaker dependent acoustic model utilizing test speech data and a hybrid estimation technique, transforming labeled speech data to create transformed speech data, utilizing the speaker dependent acoustic model and a nonlinear transformation, and adjusting a deep neural network (DNN) acoustic model, utilizing the transformed speech data.

According to another embodiment, a computer program product for adjusting a deep neural network (DNN) acoustic model comprises a computer readable storage medium having program instructions embodied therewith, wherein the computer readable storage medium is not a transitory signal per se, and where the program instructions are executable by a processor to cause the processor to perform a method comprising estimating, utilizing the processor, a speaker dependent acoustic model utilizing test speech data and a hybrid estimation technique, transforming, utilizing the processor, labeled speech data to create transformed speech data, utilizing the speaker dependent acoustic model and a nonlinear transformation, and adjusting, utilizing the processor, the DNN acoustic model, utilizing the transformed speech data.

A system according to another embodiment includes a processor, and logic integrated with the processor, executable by the processor, or integrated with and executable by the processor, the logic being configured to estimate a speaker dependent acoustic model utilizing test speech data and a hybrid estimation technique, transform labeled speech data to create transformed speech data, utilizing the speaker dependent acoustic model and a nonlinear transformation, and adjust a deep neural network (DNN) acoustic model, utilizing the transformed speech data.

DETAILED DESCRIPTION

The following description discloses several preferred embodiments of systems, methods and computer program products for adjusting a deep neural network acoustic model. Various embodiments provide a method to transform labeled speech data utilizing a speaker dependent acoustic model, and use the transformed data to adjust the deep neural network acoustic model.

The following description discloses several preferred embodiments of systems, methods and computer program products for adjusting a deep neural network acoustic model.

In one general embodiment, a computer-implemented method includes estimating a speaker dependent acoustic model utilizing test speech data and a hybrid estimation technique, transforming labeled speech data to create transformed speech data, utilizing the speaker dependent acoustic model and a nonlinear transformation, and adjusting a deep neural network (DNN) acoustic model, utilizing the transformed speech data.

In another general embodiment, a computer program product for adjusting a deep neural network (DNN) acoustic model comprises a computer readable storage medium having program instructions embodied therewith, wherein the computer readable storage medium is not a transitory signal per se, and where the program instructions are executable by a processor to cause the processor to perform a method comprising estimating, utilizing the processor, a speaker dependent acoustic model utilizing test speech data and a hybrid estimation technique, transforming, utilizing the processor, labeled speech data to create transformed speech data, utilizing the speaker dependent acoustic model and a nonlinear transformation, and adjusting, utilizing the processor, the DNN acoustic model, utilizing the transformed speech data.

In another general embodiment, a system includes a processor, and logic integrated with the processor, executable by the processor, or integrated with and executable by the processor, the logic being configured to estimate a speaker dependent acoustic model utilizing test speech data and a hybrid estimation technique, transform labeled speech data to create transformed speech data, utilizing the speaker dependent acoustic model and a nonlinear transformation, and adjust a deep neural network (DNN) acoustic model, utilizing the transformed speech data.

Now referring toFIG. 3, a storage system300is shown according to one embodiment. Note that some of the elements shown inFIG. 3may be implemented as hardware and/or software, according to various embodiments. The storage system300may include a storage system manager312for communicating with a plurality of media on at least one higher storage tier302and at least one lower storage tier306. The higher storage tier(s)302preferably may include one or more random access and/or direct access media304, such as hard disks in hard disk drives (HDDs), nonvolatile memory (NVM), solid state memory in solid state drives (SSDs), flash memory, SSD arrays, flash memory arrays, etc., and/or others noted herein or known in the art. The lower storage tier(s)306may preferably include one or more lower performing storage media308, including sequential access media such as magnetic tape in tape drives and/or optical media, slower accessing HDDs, slower accessing SSDs, etc., and/or others noted herein or known in the art. One or more additional storage tiers316may include any combination of storage memory media as desired by a designer of the system300. Also, any of the higher storage tiers302and/or the lower storage tiers306may include some combination of storage devices and/or storage media.

The storage system manager312may communicate with the storage media304,308on the higher storage tier(s)302and lower storage tier(s)306through a network310, such as a storage area network (SAN), as shown inFIG. 3, or some other suitable network type. The storage system manager312may also communicate with one or more host systems (not shown) through a host interface314, which may or may not be a part of the storage system manager312. The storage system manager312and/or any other component of the storage system300may be implemented in hardware and/or software, and may make use of a processor (not shown) for executing commands of a type known in the art, such as a central processing unit (CPU), a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), etc. Of course, any arrangement of a storage system may be used, as will be apparent to those of skill in the art upon reading the present description.

According to some embodiments, the storage system (such as300) may include logic configured to receive a request to open a data set, logic configured to determine if the requested data set is stored to a lower storage tier306of a tiered data storage system300in multiple associated portions, logic configured to move each associated portion of the requested data set to a higher storage tier302of the tiered data storage system300, and logic configured to assemble the requested data set on the higher storage tier302of the tiered data storage system300from the associated portions.

Now referring toFIG. 4, a flowchart of a method400is shown according to one embodiment. The method400may be performed in accordance with the present invention in any of the environments depicted inFIGS. 1-3 and 5-7, among others, in various embodiments. Of course, more or less operations than those specifically described inFIG. 4may be included in method400, as would be understood by one of skill in the art upon reading the present descriptions.

As shown inFIG. 4, method400may initiate with operation402, where a speaker dependent acoustic model is estimated utilizing test speech data. In one embodiment, the test speech data may include verbal data spoken by a test speaker. For example, the test speech data may include utterances such as words, sentences, etc. that are spoken by the test speaker. In another embodiment, the test speech data may include one or more acoustic characteristics of test speaker. For example, the test speech data may include one or more of environment noise, a dialect of the test speaker, an inflection of the test speaker, a pace of the test speaker, etc.

Additionally, in one embodiment, the test speaker may include a speaker whose speech is being analyzed (e.g., using automated speech recognition (ASR), etc.). In another embodiment, no transcript may be provided with the test speech data, a model may not be trained with the test speech data, etc. In yet another embodiment, estimating the speaker dependent model may include decoding the test speech data. For example, the test speech data may be decoded using a deep neural network (DNN).

Further, in one embodiment, one or more outputs of the decoding of the test speech data may be used as one or more label hypotheses for an acoustic distribution of the test speech data. In another embodiment, the one or more label hypotheses may be used to estimate the speaker dependent acoustic model. In yet another embodiment, the speaker dependent acoustic model may include a speaker dependent gaussian mixture model-hidden markov model (SD GMM-HMM) acoustic model.

Further still, in one embodiment, the speaker dependent acoustic model may be determined as part of a stochastic feature mapping (SFM) process utilizing one or more techniques. For example, the speaker dependent acoustic model may be determined utilizing maximum likelihood linear regression (MLLR). In another example, the speaker dependent acoustic model may be determined utilizing a hybrid technique that incorporates MLLR as well as a maximum a posteriori (MAP) adaptation.

Further, as shown inFIG. 4, method400may proceed with operation404, where labeled speech data is transformed to create transformed speech data, utilizing the speaker dependent acoustic model. In one embodiment, the labeled speech data may include speech data that is associated with a training speaker. For example, the labeled speech data may include one or more utterances such as words, sentences, etc. that are spoken by a training speaker. In another example, the labeled speech data may include an associated transcript, where the labeled speech data and the transcript are used to train a deep neural network (DNN) model. For instance, the labeled speech data may include associated ground truth training data, labels, transcriptions, etc. In another embodiment, the labeled speech data may be received from multiple speakers that are selected randomly or based on a metric that measures a similarity or a dissimilarity between a candidate speaker and a test speaker.

In addition, in one embodiment, the transformed speech data may include the ground truth training data, labels, transcriptions, etc. that are associated with the labeled speech data. In another embodiment, transforming the labeled speech data may be performed as part of a stochastic feature mapping (SFM) process according to one or more techniques. For example, transforming the labeled speech data may be performed utilizing a linear transformation (e.g., constrained maximum likelihood linear regression (CMLLR), etc.). In another example, transforming the labeled speech data may be performed utilizing a non-linear transformation (e.g., maximum likelihood nonlinear transformation (MLNT), etc.).

Further still, as shown inFIG. 4, method400may proceed with operation406, where a deep neural network (DNN) acoustic model is adjusted, utilizing the transformed speech data. In one embodiment, the DNN may include an artificial neural network that models one or more relationships.

Further still, in one embodiment, the DNN acoustic model may originally be trained using the labeled speech data. In another embodiment, the DNN acoustic model may be subsequently adjusted by re-training the model utilizing the transformed speech data. In yet another embodiment, the re-training of the DNN acoustic model may be performed over the entirety of a neural network, or a subset of layers of the neural network, with or without regularizations. The data for re-training may include the transformed speech data alone or may include a combination of the transformed speech data with ground-truth data and the original unlabeled test speech data with generated hypotheses.

In this way, the DNN acoustic model may be adapted for the test speech data, using labeled speech data transformed using the speaker dependent acoustic model. In yet another embodiment, the DNN acoustic model may be adjusted in a supervised environment (e.g., an environment including test speech data with ground truth labeling, etc.) or an unsupervised environment (e.g., an environment including test speech data without ground truth labeling, etc.) with a plurality of generated hypotheses. For example, the DNN adaptation may be supervised or unsupervised.

Also, in one embodiment, automatic speech recognition (ASR) may be performed, utilizing the adjusted DNN acoustic model. In another embodiment, the transformed speech data may have the same acoustic distribution as the test speech data. In this way, covariate shift may be avoided when performing ASR on the test speech data, utilizing the adjusted DNN acoustic model. Also, stochastic feature mapping (SFM) may be used to transform speech data and re-train a DNN acoustic model in order to improve the accuracy of the DNN acoustic model when performing ASR on the test speech data.

Now referring toFIG. 5, a flowchart of a method500for adjusting a deep neural network (DNN) acoustic model is shown according to one embodiment. The method500may be performed in accordance with the present invention in any of the environments depicted inFIGS. 1-4 and 6-7, among others, in various embodiments. Of course, more or less operations than those specifically described inFIG. 5may be included in method500, as would be understood by one of skill in the art upon reading the present descriptions.

As shown inFIG. 5, method500may initiate with operation502, where a speaker dependent acoustic model is estimated utilizing test speech data and maximum likelihood linear regression (MLLR).

Additionally, method500may proceed with operation504, where labeled speech data is transformed to create transformed speech data, utilizing the speaker dependent acoustic model and a linear transformation. In one embodiment, the linear transformation may include constrained maximum likelihood linear regression (CMLLR).

Also, method500may proceed with operation506, where a deep neural network (DNN) acoustic model is adjusted, utilizing the transformed speech data.

Now referring toFIG. 6, a flowchart of a method600for adjusting a deep neural network (DNN) acoustic model is shown according to one embodiment. The method600may be performed in accordance with the present invention in any of the environments depicted inFIGS. 1-5 and 7, among others, in various embodiments. Of course, more or less operations than those specifically described inFIG. 6may be included in method600, as would be understood by one of skill in the art upon reading the present descriptions.

As shown inFIG. 6, method600may initiate with operation602, where a speaker dependent acoustic model is estimated utilizing test speech data and a hybrid estimation technique. In one embodiment, the hybrid estimation technique may incorporate both maximum likelihood linear regression (MLLR) and maximum a posteriori (MAP) adaptation.

Additionally, method600may proceed with operation604, where labeled speech data is transformed to create transformed speech data, utilizing the speaker dependent acoustic model and a non-linear transformation. In one embodiment, the non-linear transformation may include maximum likelihood nonlinear transformation (MLNT).

Further, method600may proceed with operation606, where a deep neural network (DNN) acoustic model is adjusted, utilizing the transformed speech data.

Now referring toFIG. 7, a flowchart of a method700for adapting a deep neural network model using transformed speech data is shown according to one embodiment. The method700may be performed in accordance with the present invention in any of the environments depicted inFIGS. 1-6, among others, in various embodiments. Of course, more or less operations than those specifically described inFIG. 7may be included in method700, as would be understood by one of skill in the art upon reading the present descriptions.

As shown inFIG. 7, method700may initiate with operation702, where a generative speaker-dependent gaussian mixture model-hidden markov model (SD GMM-HMM) acoustic model is estimated for a test speaker. In one embodiment, an SFM implementation using maximum likelihood linear regression (MLLR) may be utilized for the SD GMM-HMM acoustic model estimation. In another embodiment, an SFM implementation using both a maximum likelihood linear regression (MLLR) and a maximum a posteriori (MAP) adaptation in a hybrid approach may be utilized for the SD GMM-HMM acoustic model estimation.

Additionally, method700may proceed with operation704, where speech data is generated by transforming a plurality of feature sequences of training speakers having ground truth labels to the SD GMM-HMM acoustic model. In one embodiment, the transformation may be carried out as part of stochastic feature mapping (SFM) utilizing maximum likelihood criterion. In another embodiment, constrained maximum likelihood linear regression (CMLLR) may be utilized to perform the feature sequence transformation. In yet another embodiment, maximum likelihood nonlinear transformation (MLNT) may be utilized to perform the feature sequence transformation.

Further, method700may proceed with operation706, where a deep neural network (DNN) model is adapted using the generated speech data. In one embodiment, the generated speech data may obey the same acoustic distribution of the test speaker and may therefore compensate for covariate shift. In this way, the adapted DNN model may include a speaker dependent DNN model.

Further still, in one embodiment, a mismatch between training and test data may give rise to covariate shift. For example, suppose one has the true acoustic distribution of a test speaker. Ideally they may sample from this distribution to generate speech data which may possess the acoustic characteristics of this speaker and use the generated speech data to adapt the original deep neural network (DNN) acoustic model. Therefore, it may be of interest to have a good estimate of acoustic distribution for a test speaker.

Also, in one embodiment, a generative SD GMM-HMM may be used to approximate the true acoustic distribution of a test speaker. In another embodiment labeled speech data may be transformed towards the SD GMM-HMM under maximum likelihood (ML) criterion. This may include stochastic feature mapping (SFM).

Table 1 illustrates an exemplary algorithm for implementing SFM-based unsupervised DNN adaptation, in accordance with one embodiment. Of course, it should be noted that the algorithm shown in Table 1 is set forth for illustrative purposes only, and thus should not be construed as limiting in any manner.

TABLE 1← a designated feature space;M ← number of test speakers;K ← number of speakers with labeled speech data;for m ← 1,... , M doDecode speech of test speaker m using original DNN anduse the decoding outputs as label hypotheses;Estimate a speaker dependent model λ(m)in feature spacefor speaker m;end forfor m ← 1,... , M dofor k ← 1,... , K doEstimate a transformationbased on the speaker de-pendent model λ(m)and all utterances from speaker kin feature space, maximizing the likelihood function(((k))|λ(m));Map utterances from speaker k to test speaker m usingin feature space;end forAdapt original DNN for test, speaker m using all-transformed utterances from K speakers;end for

In this way, an SFM-based data approach may be used to perform unsupervised DNN adaptation.

Additionally, in one embodiment, the SD GMM-HMM acoustic modelshown in Table 1 may be estimated by model space maximum likelihood linear regression (MLLR) from a speaker independent (SI) GMM-HMM. Table 2 illustrates an exemplary estimation methodology, in accordance with one embodiment. Of course, it should be noted that the estimation methodology shown in Table 2 is set forth for illustrative purposes only, and thus should not be construed as limiting in any manner.

TABLE 2{circumflex over (μ)} = Aμ + b{circumflex over (Σ)} = BTHBwhere μ and Σ are means and covariances of the SI GMM-HMM; B is the inverse of the Cholesky factor C of the inverseof the original covariance matrixΣ−1= CCT

Further, in one embodiment, the granularity of the transformation may be dynamically controlled by a regression tree depending on the amount of data available. In another embodiment, the transformationin Table 1 may have a linear form. Table 3 illustrates an exemplary linear transformation, in accordance with one embodiment. Of course, it should be noted that the linear transformation shown in Table 3 is set forth for illustrative purposes only, and thus should not be construed as limiting in any manner.

TABLE 3() = A+ bwhereis the feature sequence in feature spaceThetransformation is estimated by CMLLR:{A~,b~}=argmax{A,b}⁢⁢log⁢⁢P⁡(A⁢⁢𝒪ℋ(k)+b❘λℋ(m))

Further still, in one embodiment, speakers with labeled speech shown in Table 1 may include any speakers with labeled speech available. For example, speakers may be used from the training set from which the original DNN is trained. This may be equivalent to compensating for covariate shift by transforming the distribution of training data to make it approximately obey the distribution of the test data.

In this way, maximum likelihood linear regression (MLLR) may be used for SD model estimation and constrained maximum likelihood linear regression (CMLLR) may be used for feature sequence transformation.

Also, in one embodiment, maximum a posteriori (MAP) adaptation may converge to the SD estimate when sufficient training data is available. In another embodiment, the MAP adaptation may be local, such that only Gaussians with training samples may be adapted. The merits of an MLLR estimate and the MAP estimate may be combined into a hybrid estimate so that the resulting SD model may be closer to the true speaker manifold.

Table 4 illustrates an exemplary hybrid estimate, in accordance with one embodiment. Of course, it should be noted that the hybrid estimate shown in Table 4 is set forth for illustrative purposes only, and thus should not be construed as limiting in any manner.

TABLE 4μ^MAP=τμMLLR+∑t⁢γt⁢οtτ+∑t⁢γtwhere μMLLRis the mean prior from the MLLR-adapted model; τ isa hyperparameter that balances the new estimate and the prior;γtare the posteriors of οtat a particular Gaussian.

In addition, in one embodiment, only the means may be adapted in the MAP step. In another embodiment, the linear mapping function ofusing CMLLR may be replaced by a nonlinear mapping function. For example, a maximum likelihood nonlinear transformation (MLNT) may be used, where a DNN may be used for the nonlinear mapping. MLNT may enable a powerful mapping function for feature sequence mapping.

Table 5 illustrates an exemplary MLNT formulation, in accordance with one embodiment. Of course, it should be noted that the MLNT formulation shown in Table 5 is set forth for illustrative purposes only, and thus should not be construed as limiting in any manner.

TABLE 5MLNT is mathematically formulated as estimating a map-pping function f that maximizes the following log-likelihoodf*=maxf⁢log⁢⁢P⁡(f⁡(𝒪ℋ(m))❘λℋ(m)).

In one embodiment, the mapping function ƒ may take a form of a DNN as shown in Table 1. The parameters of ƒ may include the weights of the network whose input and output have the same dimensionality. In another embodiment, MLNT may be viewed as a nonlinear extension of CMLLR. In yet another embodiment, the MLNT implementation may be learned in a block-wise manner with CMLLR pre-training.

Furthermore, in one embodiment, a full language pack (FLP) may include 40 hours of training data with 421 speakers from the conversational speech only. WERs may be measured on the development set which has 20 hours of speech from 142 speakers.

Also, in one embodiment, the baseline DNN model may have 5 hidden layers. Each hidden layer may have 1,024 hidden units. The bottom three hidden layers may use ReLU activation functions while the top two hidden layers may use sigmoid activation functions. The softmax output layer may have 3,000 units. After a layer-wise discriminative pre-training, cross-entropy (CE) training may be performed at the frame level for 15 iterations. The CE training may use a mini-batch based stochastic gradient descent (SGD) algorithm with frame randomization. After the CE training, the DNNs may be further optimized using the Hessian-free (HF) sequence training under state-level minimum Bayes risk (sMBR) criterion.

Additionally, in one embodiment, the input to the DNN may consist of 9 frames of 40-dimensional speaker-adapted LDA features after CMLLR. The LDA features may be computed from 13-dimensional mean-normalized perceptual linear prediction (PLP) features with vocal tract length normalization (VTLN). After taking into the context information by splicing the adjacent 9 frames, the LDA may project the feature dimensionality down to 40 and it may be further decorrelated by a global semi-tied covariance (STC) matrix.

Further, in one embodiment, given the speaker-adapted LDA input features, an SI ML GMM-HMM acoustic model may be estimated in the LDA feature space right before CMLLR. The SI GMM-HMM acoustic model may have 3,000 quinphone states and 30,000 Gaussians. For each test speaker, this SI GMM-HMM may be adapted to an SD GMM-MM using the speech from the test speaker and label hypotheses. In another embodiment, the mapping from a training speaker to a test speaker may be carried out in the LDA space.

Table 6 illustrates the transformed features from the training speaker k to a test speaker m, in accordance with one embodiment. Of course, it should be noted that the transformed features shown in Table 6 are set forth for illustrative purposes only, and thus should not be construed as limiting in any manner.

TABLE 6CMLLR(m)=o(LDA(k))whereis the CMLLR transformation for the test speaker m

Further still, in one embodiment, the MLLR+MAP hybrid estimation for SD GMM-HMM may be iterated twice. The hyperparameter τ in the MAP step may be set to 10. The network for MLNT may have 2 blocks where each block has one hidden layer of 100 hidden units with hyperbolic tangent activation functions and one linear output layer.

Also, in one embodiment, under the SFM-based unsupervised adaptation, the baseline DNN may be retrained with SFM-transformed speech for each test speaker and such adapted DNNs may yield significant gains over the baseline DNN, especially at the CE stage. For example, when using MLLR for SD acoustic model estimation and CMLLR for feature mapping in SFM, the adapted DNN may obtain improvement after CE training and improvement after HF sMBR sequence training over the baseline. In another example, when using MLLR+MAP for SD acoustic model estimation and MLNT for feature mapping in SFM, the adapted DNN may obtain improvement after CE training and improvement after HF sMBR sequence training. In another embodiment, improved SFM implementation with hybrid MLLR and MAP estimate and nonlinear mapping may yield improvement after CE training and improvement after HF sMBR sequence training.

Additionally, in one embodiment, an SFM-based adaptation approach may deal with labels with errors and data sparsity, two major obstacles for unsupervised DNN speaker adaptation.

In another embodiment, label hypotheses may be used for the estimation of SD GMM-HMM acoustic models of test speakers. The GMM-HMMs may have a generative structure which may allow flexible tying of parameters, which may make them less sensitive to errors in the labels compared to discriminative models such as DNNs. In yet another embodiment, given the estimated SD acoustic models, all the generated speech feature sequences transformed from training speakers may have ground-truth labels, which may benefit the adaptation of DNNs.

Further, in one embodiment, speakers with labeled speech may be used for the mapping. As a result, there may be an unlimited amount of speech data that may be transformed, which may mitigate any data sparsity issue. In another embodiment, in the experiments all speakers in the training set may be transformed towards the SD acoustic model of each test speaker. This may amount to mapping all training speakers' “voices” to each of the test speakers. This may compensate for the covariate shift. As a result, each test speaker may have about 40 hours of speech and the adapted DNN may be viewed as an SD DNN. Depending on the amount of transformed data, the original DNN may also be partially adapted.

Further still, in one embodiment, the adaptation may be parallelized by speakers and for each speaker it may be parallelized both at CE and HF sMBR sequence training stages. The total workload of this approach may be linearly proportional to the number of speakers in the test set.

In this way, an unsupervised DNN speaker adaptation approach may be implemented that may be based on stochastic feature mapping. To deal with covariate shift, a generative speaker dependent GMM-HMM acoustic model may first be estimated for each test speaker, and speakers in the training set with labeled speech data may be mapped to the test speaker. The original DNN acoustic model may be retrained using the transformed speech with ground-truth labels. One implementation may use MLLR for estimating SD GMM-HMM and CMLLR for feature mapping, and another implementation may use a hybrid MLLR/MAP estimate for SD GMM-HMM and a DNN-based nonlinear transformation for feature mapping. This SFM-based unsupervised DNN adaption may obtain significant improvements over a DNN baseline using speaker-adapted LDA input features.

More specifically, a data approach to unsupervised speaker adaptation of DNNs may be enabled. For example, a generative speaker-dependent (SD) GMM-HMM model may first be estimated based on label hypotheses for the acoustic distribution of each test speaker. Given this target distribution, speech data may be generated by transforming feature sequences of the training speakers with ground-truth labels to the SD acoustic model, which may be carried out by stochastic feature mapping (SFM) under the maximum likelihood (ML) criterion. The original DNN may then be adapted using the generated speech data which may approximately obey the same acoustic distribution of the test speaker and may therefore compensate for covariate shift. This approach may generate an unlimited amount of adaptation data with ground-truth labels. As a result, the adapted DNN may be viewed as an SD DNN.