Domain adaptation refers to the task of adapting models trained on one domain to other domains. In the general setting, models are trained in the source domain and tested on the target domain. The source domain may or may not have overlaps with the target domain. The mismatch between the training and the test conditions causes the task performance to deteriorate, because generalization guarantees rely on the assumption that the training and test samples come from the same underlying distribution. Domain adaption in the most general case is possible under some assumptions, but deemed challenging [1, 2].
Domain adaptation for speech recognition is particularly difficult considering the mismatch in speakers, speaking styles, noise types, and room acoustics etc. There has been significant success in dealing with speaker mismatch, for example, adapting a speaker-independent model to a known speaker or even adapting to an unknown speaker [3, 4]. Developing speech recognizers that are robust to many noise types is more challenging, and in theory it is impossible to have a model that is robust to any adversarial noise . It is, however, still possible to design speech recognizers that are robust to natural noise types that occur in our daily lives. Significant progress has been made in this direction, especially when the noise types are known at training time, for example, with speech enhancement techniques or multi-condition training [6, 7, 8].
This paper focuses on the task of adapting speech recognizers trained on close-talking speech to distant speech. Distant speech recognition is itself a difficult task . The difficulty is often attributed to reverberation, i.e., weaker copies of the original speech signals. Early reverberation is considered easy to handle, because convolving shifted impulses in the time domain is nothing but a constant scaling function on the power spectrum. Late reverberation, on the other hand, is not limited to single short-term spectra and cannot be approximated well with shifted impulses. As a result, the speech is corrupted with a type of noise that is highly correlated with the speech from the past. Important effort has been devoted to training models directly on distant speech . Other solutions for distant speech recognition include using multiple microphones [11, 12, 13], speech enhancement techniques [14, 8], and data augmentation [15, 16]. It is also unclear if the degradation in performance is really due to reverberation and not due to other causes, such as the difference in gain levels. We investigate this by training models on data augmented with simulated reverberation.
There has been some work in adapting speech recognizers to distant speech [10, 17, 18, 19]. However, different studies use different settings, for example, whether it is allowable to use parallel data to train models, or whether we have access to labels in the other domain. In this paper, we consider various settings, their requirements, and the performance of speech recognizers of a fixed architecture. The purpose of this paper is to quantify and characterize the gap of these settings, and set up the basis for studying domain adaptation for distant speech recognition. Note that we do not consider the online adaptive setting, a common scenario for speaker adaptation [3, 4, 20, 21], where we have a small amount of labeled data to adapt to the target domain.
2 Domain Adaptation
In this section, we summarize the approaches and their requirements for adapting speech recognizers from close-talking speech to distant speech. In the general setting, let the input space be and the output space be . For speech recognition,
is the set of sequences of log Mel filterbank feature vectors, andis the set of word sequences. We have two unknown data distributions and over representing the source and the target domain. In the following discussion, we refer to close-talking speech as the source domain and distant speech as the target domain.
2.1 Speech enhancement
To reduce the mismatch between domains, a simple approach is to transform data from the target domain to the source domain where the recognizer is trained. We assume there is an unknown distortion function such that for . The goal is to find a function such that for . For speech processing, transforming noisy speech to clean speech is referred to as speech enhancement.
In general, speech enhancement has a broader goal: transforming signals so that the speech stands out and becomes more audible. This typically involves removing noise (though sometimes adding noise can improve intelligibility ). We focus on the limited sense of enhancement, making speech closer to its clean counterpart while ignoring intelligibility. We assume we have access to a parallel data set where for . The objective is to approximate the clean speech given the noisy speech by minimizing the Euclidean distance for . Minimizing this objective for speech enhancement was first proposed in 
and is explored in the context of neural networks in. Deep neural networks are particularly suitable for speech enhancement without posing any assumptions on the noise types. Modern treatments with deep networks are studied in [25, 6, 26, 8].
Once a model for speech enhancement is trained, we enhance the speech signal prior to doing speech recognition, i.e., using instead of as the input to the speech recognizer. Training speech enhancement models requires parallel data in both domains, which makes data collection costly. However, this approach does not need transcripts for the parallel data. Speech recognizers trained on the source domain can also be reused without additional training.
2.2 Multi-condition training
Another simple approach to reduce the mismatch between domains is to use the data from the target domain during training. Suppose we have and where and are the numbers of samples for the two data sets. Models are simply on the data set . If the performance on the target domain is the only concern, we can always discard and train models only on . For noise-robust speech recognition, training models on different noise conditions is referred to as multi-condition training or multi-style training. Multi-condition training can be traced back to , and has been shown to reduce mismatch for different noise conditions . Deep neural networks work particularly well with multi-condition training due to the large model capacity [7, 10].
Multi-condition training requires labeled data in both domains, so data collection can be costly. Additional training, either from scratch or from a pre-trained model, is required. When the model capacity is large enough, a single model is able to cover multiple domains. However, the training time scales linearly with the amount of data.
2.3 Data augmentation
As a special case of multi-condition training, data augmentation transforms data from the source domain to the target domain (i.e., the opposite of speech enhancement). This typically involves corrupting the clean data with different noise types or transforming the clean data with simulators, such as convolving the clean speech with room impulse responses. Formally, we assume we have a generator distribution . Let where for and some data set . We train models on the data set . This approach is expected to work well if the generator is able to the match the target domain, i.e., for and , either or for an unknown distortion function such that
. Data augmentation was originally designed as a regularization technique for learning transformation invariant features, and has been successful in image classification tasks with convolutional neural networks[29, 30, 31]. Data augmentation has been applied to speech recognition in [32, 16, 15].
Data augmentation is suitable when the simulation of noise or other factors is simple, for example, perturbing vocal tract lengths , perturbing speed , and simulating reverberation . Data from the target domain is not required. However, the training time scales linearly with the amount of generated data.
2.4 Unsupervised domain adaptation with autoencoders
Finding similarities between the target and the source domains is yet another way to tackle domain mismatch. For example, we assume a common distribution for linguistic content, such as English utterances. The source and the target domain can still have their own nuisance factors depending on speakers and channels. Each domain can be modeled as a generative process where an utterance is first sampled from the shared distribution and is transformed according to the nuisance factors. Since the two domains are symmetric, we describe the process in one domain ; the other domain follows the same generative story. For example, we can have where 0 denotes the source domain and 1 denotes the target domain. Suppose an utterance from domain has segments . Each segment is generated by a domain-independent vector and a domain-dependent vector . The domain-independent vector encodes the linguistic content where is the shared distribution for all domains, while the domain-independent vector encodes the nuisance factors, such as speakers and channels, specific to domain . The segment is then generated from a function that depends on and
We use factorized hierarchical variational autoencoders (FHVAE)  to model the above generative process with two inference networks , . Without any further constraints, and are fully exchangeable. To make sure captures the nuisance factors, we constrain the ’s from the same utterance to be similar while leaving unconstrained, because the nuisance factors largely remain unchanged within the same utterance. In addition, there is a loss enforcing to be predictive of the utterance identity.
After training the FHVAE on all data combined, we use the inference network to obtain the vectors that encode the linguistic contents and discard the vectors for the nuisance factors. Speech recognizers are trained on these new set of features. This approach does not require parallel data from both domains, and the data does not need to be labeled. However, tuning FHVAEs might be difficult. If the model has too many parameters for reconstruction, we might obtain a trivial identity function. If the weight between reconstruction and the KL-divergence is tuned, we do not have a fixed objective to compare different FHVAEs.
In order to have a fair comparison for all the settings, we conduct experiments on the AMI data set, where parallel recordings and labels are available for both the close-talking and the distant speech domains. The AMI data set is a meeting corpus with around 100 hours of conversational non-native English speech. The meetings are recorded in a controlled environment with independent headset microphones (IHM) on each speaker and multiple distant microphones. The audio streams from different microphones are aligned with beamforming. We take the aligned recordings from the IHMs and one specific distant microphone, referred to as the single distant microphone (SDM), for our experiments. To avoid excessively querying the standard test set, we do not report numbers on the standard test set. Instead, we use 90% of the training set for training, leave 10% for development, such as step size tuning and early stopping, and only report word error rates (WERs) on the standard development set.
, we use 80-dimensional log Mel filterbank features, and train two speaker-adaptive hidden Markov models (HMM), one for IHM and one for SDM. We obtain forced alignments of the tied HMM states (also known as pdf-ids) for both IHM and SDM recordings with the corresponding systems, and use the pdf-ids as targets for acoustic model training. We use eight-layer time-delay neural networks (TDNNs) with 1000 hidden hidden units per layer as our acoustic models. Following, the context sizes of the TDNNs from layer one to seven are , where indicates the summation of hidden vectors at time , , and . Formally, to compute the hidden layer from with context , we have
Note that in contrast to the standard recipe, we only use the 80-dimensional log Mel features as input without appending the i-vectors.
3.1 Baseline and multi-condition training
Since we are interested in adapting models trained on close-talking speech to distant speech, we train two TDNNs, one on IHM and one on SDM, and test them on utterances from both IHM and SDM. We use stochastic gradient descent (SGD) with a fixed step size 0.025 and a mini-batch size of 1 utterance to optimize the cross entropy for 20 epochs. Gradients are clipped to norm 5. We choose the best performing model from the 20 epochs based on the frame error rates, and train it for another 5 epochs with step sizedecayed by 0.75 after each epoch. Results are shown in Table 1. The WER increases from 27.4% to 70.3% when using a close-talking model on distant speech. Note that in the SDM setting, the WER of IHM is lower than the that of SDM, consistent with the results reported in [17, 36]. We also confirm the improvement reported in , training models on SDM data while using IHM alignments. For consistency, we use IHM alignments for the rest of the experiments.
For multi-condition training, we train and tune TDNNs on both IHM and SDM combined. The training procedure remains the same except that we use a smaller initial step size 0.01. Results are shown in Table 1. The TDNN is able to match the results on both domains.
|SDM (IHM alignments)||IHM||39.2|
|SDM (IHM alignments)||SDM||46.6|
|IHM + SDM||IHM||27.2|
|IHM + SDM||SDM||45.3|
3.2 Data augmentation with simulated reverberation
To investigate the impact of reverberation on distant speech recognition, we use the image method described in  to create a set of simulated room impulse responses (RIRs) with different rectangular room sizes, speaker positions, and microphone positions, as proposed in . Three sets of rooms (, , and ) are generated by uniformly sampling the width , length and height (in meters) in set-wise ranges (where
stands for a uniform distribution betweenand ):
For each room, the speed of sound is set to m/sec, and the wall, ceiling and floor reflection coefficient is sampled from a uniform distribution between and . For each set, 200 rooms are sampled, 100 RIRs are obtained for both the source and microphone positioned randomly in the room, leading to a total of 60,000 simulated RIRs for all sets. For each utterance in the dataset, one of these RIRs is selected randomly and convolved with the clean speech.
We train TDNNs on IHM and IHM corrupted with simulated reverberation the same way we train multi-conditioned models in the previous section. We test the TDNNs on the IHM data corrupted with reverberation and SDM. Results are shown in Table 2. The degradation due to reverberation is not as severe compared to that of SDM. Training TDNNs with the additional data does help generalize to the SDM domain. However, the improvement is far from closing the gap, suggesting that reverberation might not be the major cause of the performance degradation.
|IHM + IHM-r||IHM||28.7|
|IHM + IHM-r||IHM-r||43.7|
|IHM + IHM-r||SDM||63.3|
3.3 Speech enhancement
For speech enhancement, we use the same TDNN architecture without the final softmax. TDNNs are trained to predict the features of IHM utterances given the corresponding features of SDM utterances, while being an identity function given features of IHM utterances. The training set in this case is the IHM and SDM combined. The mean squared error is minimized using the same training procedure with an initial step size of 0.01. After training the enhancement model, we take the baseline model trained on IHM and test it on the enhanced data. Results are shown in Table 3. The WER on the enhanced SDM (SDM-e) is significantly reduced from 70.3% to 54.2%, while maintaining the WER on the IHM domain.
Again, to investigate how reverberation plays a role in distant speech recognition, we train a dereveberation TDNN on the IHM data corrupted with reverberation while being an identity function on the clean IHM data. We then evaluate the baseline TDNN trained on IHM with the dereveberated data. Results are shown in Table 3. We see some amount of improvement from 59.3% (in Table 2) to 53.1%, suggesting that the TDNN is able to perform blind dereverberation. However, the improvement is not as large as the multi-condition TDNN, suggesting that blind dereverberation is in itself a challenging task. We also evaluate the dereverberation model on SDM, and find no improvement over the baseline. This again suggests that the domain mismatch between IHM and SDM might not be due to reverberation but some other types of mismatch.
3.4 Unsupervised domain adaptation with FHVAEs
For unsupervised domain adaptation, we train a FHVAE by minimizing the discriminative segmental variational lower bound  with a factor for the utterance discriminative loss. The FHVAE consists of two encoders and one decoder. One encoder is for the shared distribution (representing linguistic content) and the other is for the domain-specific distribution (representing nuisance factors). The decoder takes the output vectors from both encoders and reconstructs the input features. Inputs to an FHVAE are 20 frames of 80-dimensional log Mel features. Both encoders are LSTM networks 
with 256 memory cells that process one frame at each step, followed by an affine transform layer that takes the LSTM output from the last step and predicts the posterior mean and log variance of the corresponding latent variables. We use an LSTM decoder with 256 memory cells, where the LSTM output from each step is passed to an affine transform layer to predict the mean and variance of a frame. The Adam optimizer is used with , , , and initial learning rate of . Early stopping is done by monitoring the evidence lower bound on the development set.
After the FAVAE is trained, we use the encoder for the shared distribution to produce features. A feature vector is generated at each time point by taking a 20-frame segment centered at the current time point and feeding it forward into the encoder. Following 
, since the generated feature sequence is 19 frame shorter, we repeat the first and the last feature vector at each end to match the original length. The hidden vectors are then normalized by subtracting the mean and dividing by the standard deviation computed over the training set. TDNNs are trained on the produced feature vectors with the same training procedure as in previous sections. Since the distribution is modeled as a Gaussian, we use the Gaussian mean vectors and have the option to include the log-variance vectors as features. Results are shown in Table4. While there is a small amount of degradation in the IHM domain, we see an improvement from 70.3% to 61.8% in the SDM domain. This suggests that the SDM features produced by the FHVAE are closer to IHM in the latent space. The improvement is even larger than data augmentation with simulated reverberation. However, we find that including the log-variance as features might not help adapting to the target domain. This needs further investigation.
In this work, we review several approaches, including speech enhancement, data augmentation, and autoencoders, to bridge the gap from close-talking speech recognition to distant speech recognition from a domain adaptation perspective. We find that all approaches are able to produce models that are more robust than the baseline. Multi-condition training gives the best results among all approaches, but it also has the most stringent requirement, requiring labeled data in all domains. Speech enhancement comes second but also has a stringent requirement, requiring parallel unlabeled data. Data augmentation has the potential to match the performance of multi-condition training. However, it requires the data generation process to cover the condition of the target domain. Unsupervised domain adaptation with autoencoders is promising, achieving better results than data augmentation with simulated reverberation while only requiring independent unlabeled data from both domains. Finally, the results suggest that the mismatch between IHM and SDM in the AMI data set is probably less about reverberation and has some other factors, such as cross talking, that need to be studied further.
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