Matrix variate Kummer‐Dirichlet distributions

Gupta, Arjun K.; Cardeño, Liliam; Nagar, Daya K.

doi:10.1155/s1110757x0100701x

Cited by 22 publications

(31 citation statements)

References 6 publications

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“…The Gaussian distribution of random matrices is well understood [4]. A typical example of its application in speech recognition is maximum a posteriori linear regression (MAPLR) [5] for speaker adaptation, in which a matrix variate prior was used for the linear regression transformation matrix.…”

Section: Matrix Variate Gaussian Priormentioning

confidence: 99%

Maximum a posteriori adaptation of subspace Gaussian mixture models for cross-lingual speech recognition

Ghoshal

Renals

2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper concerns cross-lingual acoustic modeling in the case when there are limited target language resources. We build on an approach in which a subspace Gaussian mixture model (SGMM) is adapted to the target language by reusing the globally shared parameters estimated from out-of-language training data. In current cross-lingual systems, these parameters are fixed when training the target system, which can give rise to a mismatch between the source and target systems. We investigate a maximum a posteriori (MAP) adaptation approach to alleviate the potential mismatch. In particular, we focus on the adaptation of phonetic subspace parameters using a matrix variate Gaussian prior distribution. Experiments on the GlobalPhone corpus using the MAP adaptation approach results in word error rate reductions, compared with the cross-lingual baseline systems and systems updated using maximum likelihood, for training conditions with 1 hour and 5 hours of target language data.

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Section: Matrix Variate Gaussian Priormentioning

confidence: 99%

Maximum a posteriori adaptation of subspace Gaussian mixture models for cross-lingual speech recognition

Ghoshal

Renals

2012

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…The Gaussian distribution of random matrices is well understood [36]. A typical example of its application in speech recognition is maximum a posteriori linear regression (MAPLR) [37] for speaker adaptation, in which a matrix variate prior is used for the linear regression transformation matrix.…”

Section: A Matrix Variate Gaussian Priormentioning

confidence: 99%

Cross-Lingual Subspace Gaussian Mixture Models for Low-Resource Speech Recognition

Ghoshal

Renals

2014

IEEE/ACM Trans. Audio Speech Lang. Process.

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This paper studies cross-lingual acoustic modelling in the context of subspace Gaussian mixture models (SGMMs). SGMMs factorize the acoustic model parameters into a set that is globally shared between all the states of a hidden Markov model (HMM) and another that is specific to the HMM states. We demonstrate that the SGMM global parameters are transferable between languages, particularly when the parameters are trained multilingually. As a result, acoustic models may be trained using limited amounts of transcribed audio by borrowing the SGMM global parameters from one or more source languages, and only training the state-specific parameters on the target language audio. Model regularization using 1 -norm penalty is shown to be particularly effective at avoiding overtraining and leading to lower word error rates. We investigate maximum a posteriori (MAP) adaptation of subspace parameters in order to reduce the mismatch between the SGMM global parameters of the source and target languages. In addition, monolingual and cross-lingual speaker adaptive training is used to reduce the model variance introduced by speakers. We have systematically evaluated these techniques by experiments on the GlobalPhone corpus.

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“…Note that even though Jun et al [2005] claim that in this case the expectation E(C) with respect to Eq. (4) is C 0 , this is not the case unless, k ¼ 3r 0 + 2, which is seen by calculating EðCÞ ¼ r0 kÀ2r0À2 C 0 [Gupta and Nagar, 2000]. However, our model is not overly sensitive to the estimated noise covariance C 0 due to the SVD strategy, so we used the value of k ¼ 4r 0 , giving…”

Section: The Noise Covariance Priormentioning

confidence: 99%

Bayesian inverse analysis of neuromagnetic data using cortically constrained multiple dipoles

Auranen¹,

Nummenmaa²,

Hämäläinen

et al. 2007

Human Brain Mapping

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A recently introduced Bayesian model for magnetoencephalographic (MEG) data consistently localized multiple simulated dipoles with the help of marginalization of spatiotemporal background noise covariance structure in the analysis [Jun et al., (2005): Neuroimage 28:84-98]. Here, we elaborated this model to include subject's individual brain surface reconstructions with cortical location and orientation constraints. To enable efficient Markov chain Monte Carlo sampling of the dipole locations, we adopted a parametrization of the source space surfaces with two continuous variables (i.e., spherical angle coordinates). Prior to analysis, we simplified the likelihood by exploiting only a small set of independent measurement combinations obtained by singular value decomposition of the gain matrix, which also makes the sampler significantly faster. We analyzed both realistically simulated and empirical MEG data recorded during simple auditory and visual stimulation. The results show that our model produces reasonable solutions and adequate data fits without much manual interaction. However, the rigid cortical constraints seemed to make the utilized scheme challenging as the sampler did not switch modes of the dipoles efficiently. This is problematic in the presence of evidently highly multimodal posterior distribution, and especially in the relative quantitative comparison of the different modes. To overcome the difficulties with the present model, we propose the use of loose orientation constraints and combined model of prelocalization utilizing the hierarchical minimum-norm estimate and multiple dipole sampling scheme.

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Matrix variate Kummer‐Dirichlet distributions

Cited by 22 publications

References 6 publications

Maximum a posteriori adaptation of subspace Gaussian mixture models for cross-lingual speech recognition

Maximum a posteriori adaptation of subspace Gaussian mixture models for cross-lingual speech recognition

Cross-Lingual Subspace Gaussian Mixture Models for Low-Resource Speech Recognition

Bayesian inverse analysis of neuromagnetic data using cortically constrained multiple dipoles

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