deep neural networks for acoustic modeling in speech recognition

Introduction

Classical speech recognition systems use hidden Markov models (HMMs) to model the temporal variations and Gaussian mixture models (GMMs) to determine the likelihood of each state of each HMM given an acoustic observation. The speech signal in the classical systems are represented by a series of Mel-frequency cepstral coefficients (MFCCs) or perceptual linear predictive coefficients (PLPs) extracted from overlapping short windows of the raw speech signal. Although GMMs are quite flexible and are fairly easy to train using the Expectation Maximization (EM) algorithm, they are inefficient when modelling data that lie close to a nonlinear manifold which is the case for the speech data. Deep Neural Networks (DNNs) don't suffer from the same shortcoming, hence they can learn much better models than GMMs. Over the past few years, training DNNs has become possible thanks to the advancements in machine learning and computer hardware, which makes it possible to replace GMMs with DNNs in the speech recognition systems. DNNs are proved to outperform GMMs in both small and large vocabulary speech recognition tasks.

Interfacing a DNN with an HMM

HMM model requires the likelihoods of the observations [math]\displaystyle{ p(AcousticInput|HMMstate) }[/math] for running the forward-backward algorithm or for computing a Viterbi alignment. DNNs output the posteriors [math]\displaystyle{ p(HMMstate|AcousticInput) }[/math] which can be converted to scaled version of the likelihood by dividing them by [math]\displaystyle{ p(HMMstate) }[/math], where [math]\displaystyle{ p(HMMstate) }[/math] is the HMM states frequencies in the training data. The conversion from the posteriors to the likelihoods is important when the training labels are highly unbalanced.

Phonetic Classification and Recognition on TIMIT

TIMIT is an acoustic-phonetic countinuous speech corpus that has been widely used as a benchmark data set for the speech recognition systems. DNN-HMM systems outperformed the classical GMM-HMM systems. The first successful attempt for building a DNN-HMM speech recognition system was published in 2009 by Mohamed et. al.<ref name=firstDBN> A. Mohamed, G. Dahl, and G. Hinton, “Deep belief networks for phone recognition,” in Proc. NIPS Workshop Deep Learning for Speech Recognition and Related Applications, 2009. </ref>, they reported a significant improvement in the accuracy over the state-of-the-art DNN-HMM systems at that time. It was found that the structure of the DNN (i.e. number of hidden layers, and number of hidden units per layer) has little effect on the accuracy, which made it possible to focus more on learning the metaparameters of the DNN. Details of the learning rates, stopping criteria, momentum, L2 weight penalties and minibatch size, pretraining, and fine-tuning can be found in <ref name=tuning_fb_DBN>A. Mohamed, G. Dahl, and G. Hinton, “Acoustic modeling using deep belief networks,” IEEE Trans. Audio Speech Lang. Processing, vol. 20, no. 1, pp. 14–22, Jan. 2012.</ref>.

Using Filter-Bank Features

MFCC features are commonly used in the GMM-HMM systems because they provide uncorrelated features, which is important to avoid using full covariance GMMs. Some of the acoustic information is lost due to using MFCCs. DNNs on the other hand can work with correlated features which opened the room for using filter-bank features. It was found that using filter-bank features with DNNs improved the accuracy by 1.7% <ref name=tuning_fb_DBN></ref>.

Fine-Tuning DNNs To Optimize Mutual Information

In the experiments mentioned earlier this section, the system were tuned to optimize the per frame cross entropy or the log posterior probablity [math]\displaystyle{ p(l_t|v_t) }[/math]; where [math]\displaystyle{ l_t }[/math] is label at time [math]\displaystyle{ t }[/math], and [math]\displaystyle{ v_t }[/math] is the features at the same time step. The transition probabilities and the language models were tuned independently using the HMM framework. The DNN can be tuned to optimize the conditional probability [math]\displaystyle{ p(l_{1:T}|v_{1:T}) }[/math], this is done for the softmax layer only and by fixing the parameters of the hidden layers [math]\displaystyle{ h }[/math].

[math]\displaystyle{ (l_{1:T}|v_{1:T}) = p(l_{1:T}|h_{1:T}) = \frac{\exp(\sum_{t=1}^T\gamma_{ij} \phi_{ij}(l_{t-1},l_t) + \sum_{t=1}^T\sum_{d=1}^D \lambda_{l_t,d} h_{td})}{Z(h_{1:T})} }[/math]

Where [math]\displaystyle{ \phi_{i,j}(l_{t-1},l_t) }[/math] is the transition feature and it takes a value of one if [math]\displaystyle{ l_{t-1} = i }[/math] and [math]\displaystyle{ l_{t} = j }[/math] and zero otherwise, [math]\displaystyle{ \gamma_{ij} }[/math] is the parameter associated with the transition feature, [math]\displaystyle{ \lambda }[/math] are the weights of the softmax layer. [math]\displaystyle{ \gamma,\lambda }[/math] are tuning using gradient descent, and the experiments show the fine tuning DNNs to optimize the mutual information improved the accuracy by 5% relative on TIMIT data set <ref name=finetuningDNN> A. Mohamed, D. Yu, and L. Deng, “Investigation of full-sequence training of deep belief networks for speech recognition,” in Proc. Interspeech, 2010, pp. 2846–2849. </ref>.

DNNs and GMMs

Compariosons among the reported speaker-independent (SI) phonetic error rate (PER) results on TIMIT core test set with 192 sentences.

Method	PER
CD-HMM	27.3%
Augmented Conditional Random Fienlds	26.6%
Randomly Initialized Recurrent Neural Nets	26.1%
Bayesian Triphone GMM-HMM	25.6%
Monophone HTMs	24.8%
Heterogeneous Classifiers	24.4%
Monophone Randomly Initialized DNNs (Six Layers)	23.4%
Monophone DBN-DNNs (Six Layers)	22.4%
Monophone DBN-DNNs with MMI Training	22.1%
Triphone GMM-HMMs DT W/BMMI	21.7%
Monophone DBN-DNNs on FBank (Eight Layers)	20.7%
Monophone MCRBM-DBN-DNNs On FBank (Five Layers)	20.5%
Monphone Convolutional DNNs On Fbank (Three Layers)	20.0%

References

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