## LU FACTORIZATION FOR FEATURE TRANSFORMATION Patrick Nguyen

### BibTeX

@MISC{Rigazio_lufactorization,

author = {Luca Rigazio and Christian Wellekens and Jean-claude Junqua},

title = {LU FACTORIZATION FOR FEATURE TRANSFORMATION Patrick Nguyen},

year = {}

}

### OpenURL

### Abstract

Linear feature space transformations are often used for speaker or environment adaptation. Usually, numerical methods are sought to obtain solutions. In this paper, we derive a closed-form solution to ML estimation of full feature transformations. Closed-form solutions are desirable because the problem is quadratic and thus blind numerical analysis may converge to poor local optima. We decompose the transformation into upper and lower triangular matrices, which are estimated alternatively using the EM algorithm. Furthermore, we extend the theory to Bayesian adaptation. On the Switchboard task, we obtain 1.6 % WER improvement by combining the method with MLLR, or 4 % absolute using adaptation. 1.

### Citations

434 | Maximum Likelihood Linear Transformations for HMM-Based Speech Recognition
- Gales
- 1997
(Show Context)
Citation Context ...e know that stationary points of the gradient correspond to a maximum or minimum in8 . This seemingly simple problem is a multidimensional quadratic equation and has no closedform solution in general =-=[3]-=-. Gales [3] assumes rows to be almost independent and optimizes row by row. Gopinath [2] points out that half of the function is quadratic and therefore suitable for conjugate gradient descent. Digila... |

103 | Maximum likelihood modeling with Gaussian distributions for classification
- Gopinath
- 1998
(Show Context)
Citation Context ...smatch. They are naturally integrated into the SAT paradigm toward offering compact models for speech recognition. The analytical mathematics are somewhat related to semitied covariances [1] and MLLT =-=[2]-=-. Both acknowledge the absence of a closed-form solution in the general case and proceed to define numerical expedient for that ailment. Numerical methods are sensitive to conditioning and extra care ... |

94 | Fast speaker adaptation using constrained estimation of Gaussian mixtures
- Digalakis, Rtischev, et al.
- 1995
(Show Context)
Citation Context ...les [3] assumes rows to be almost independent and optimizes row by row. Gopinath [2] points out that half of the function is quadratic and therefore suitable for conjugate gradient descent. Digilakis =-=[4]-=- advocates iterative numerical methods but cites none in particular. Bilmes [5] uses a unitary matrices, for which the Jacobian disappears. We present a solution that can be seen as a combilation of [... |

39 | Sparse Inverse Covariance Matrices
- Bilmes, “Factor
- 2000
(Show Context)
Citation Context ...h [2] points out that half of the function is quadratic and therefore suitable for conjugate gradient descent. Digilakis [4] advocates iterative numerical methods but cites none in particular. Bilmes =-=[5]-=- uses a unitary matrices, for which the Jacobian disappears. We present a solution that can be seen as a combilation of [4] and [5]. [0 =?*@A B A WD)E\0 ,']T^_Ù R ?RaT ? 0CUbP)RaT Z: 8 Z =?*@A B A WD... |

8 | EWAVES: an efficient decoding algorithm for lexical tree based speech recognition
- Nguyen, Rigazio, et al.
(Show Context)
Citation Context ...el containing compound words and frequent abbreviations [7]. It was kindly provided to us by Andreas Stolcke of SRI. It contains 34k words, 5M bigrams, and 12M trigrams. Our recognizer, called EWAVES =-=[8]-=-, is a lexical-tree based, gender-independent, word-internal context-dependent, trigram Viterbi decoder with bigram LM lookahead. For adaptation, we use the transcription of the first pass. The second... |

4 | Adapting Semi-Tied Full-Covariance Matrix HMMs (tr298
- Gales
- 1997
(Show Context)
Citation Context ...or speaker mismatch. They are naturally integrated into the SAT paradigm toward offering compact models for speech recognition. The analytical mathematics are somewhat related to semitied covariances =-=[1]-=- and MLLT [2]. Both acknowledge the absence of a closed-form solution in the general case and proceed to define numerical expedient for that ailment. Numerical methods are sensitive to conditioning an... |

3 |
results
- Swanson, Martin, et al.
(Show Context)
Citation Context ...ior information. 4.1. Conditions 4. EXPERIMENTS To validate our algorithm, we used the Switchboard conversational telephone speech database. We report results on the first evaluation test set of 2001 =-=[6]-=-, which contains 20 conversations from the Switchboard-I database. The acoustic frontend uses 27 PLP coefficients (8 pole model plus energy, and their first and second derivatives), which were normali... |