## Linear Gaussian models for speech recognition (2004)

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Venue: | CAMBRIDGE UNIVERSITY |

Citations: | 16 - 0 self |

### BibTeX

@TECHREPORT{Rosti04lineargaussian,

author = {Antti-Veikko Ilmari Rosti},

title = {Linear Gaussian models for speech recognition},

institution = {CAMBRIDGE UNIVERSITY},

year = {2004}

}

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### Abstract

Currently the most popular acoustic model for speech recognition is the hidden Markov model (HMM). However, HMMs are based on a series of assumptions some of which are known to be poor. In particular, the assumption that successive speech frames are conditionally independent given the discrete state that generated them is not a good assumption for speech recognition. State space models may be used to address some shortcomings of this assumption. State space models are based on a continuous state vector evolving through time according to a state evo-

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Citation Context ...mance, mathematically this technique conflicts with the independence assumption. This independence assumption is widely thought to be the major drawback of the use of HMMs for speech recognition (eg. =-=[22, 35, 58, 100, 103]-=-). State space models may be used to address the shortcomings of HMM based speech recognition. State space models are based on a hidden continuous state evolution process and an observation process wh... |

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Citation Context ...ords in the correct transcription [127]. (2.32) When comparing the performance of different systems, it is useful to have a measure of confidence in the relative difference in the WER. McNemar’s tes=-=t [42]-=- is used in this work to yield the percentage probability, P (MINUUE|TUUE), where MINUUE is the minimum number of unique utterance errors of two systems under consideration and TUUE is the total numbe... |

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Citation Context ...the FAHMM does not address the independence assumption. However, it generalises many standard covariance modelling schemes such as the shared factor analysis [46] and semi-tied covariance matrix HMMs =-=[32]-=-. Algorithms to optimise the FAHMM parameters and to use FAHMMs for speech recognition are presented together with various schemes to improve their efficiency. Second, a model based on linear first-or... |

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Citation Context ...rmance than ML. Discriminative optimisation criteria include maximum mutual information (MMI) [4], minimum classification error rate (MCE) [63], frame discrimination [67] and minimum phone error rate =-=[104]-=- of which MMI and MPE have been the most successful in speech recognition [47, 126]. In comparison to ML training, the discriminative methods require recognition runs to be carried out during training... |

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Citation Context ...ly complex models, suggests that there may be inherent deficiencies in the modelling paradigm. This work concentrates on the problems associated with acoustic modelling. The Hidden Markov model (HMM) =-=[60]-=- is the most popular and successful choice of acoustic model in modern speech recognisers. However, the HMM is based on assumptions which are not appropriate for modelling speech signals [35, 58]. The... |

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Citation Context ...namic Models Dynamic linear Gaussian models and the corresponding static models are illustrated in Figure 3.8. Dynamic models with factor analysis observation process include linear dynamical systems =-=[22, 23, 39, 87, 100, 117]-=-, mixture of linear dynamical systems [111] and switching state space model [40, 91] as well as different variations of factor analysed HMMs presented later in this 4 Mixture weights are not included ... |

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Citation Context ... be bounded as follows log p(O) ≥ � � p(O, Z, m1) q(Z, m1) log q(Z, m1) dm1 (4.15) ∀Z where Z is a matrix of mixture indicators znm defined in Appendix C. Following the derivations in various =-=studies [2, 90], the vari-=-ational approximation is constrained to factor q(Z, m1) = q(Z)q(m1) where the mixture indicator probability may be further simplified to � q(znm) ∝ P (ω = m) exp � � q(m1) log p(on|ω = m, m1... |

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Citation Context ...ure 3.8. Dynamic models with factor analysis observation process include linear dynamical systems [22, 23, 39, 87, 100, 117], mixture of linear dynamical systems [111] and switching state space model =-=[40, 91]-=- as well as different variations of factor analysed HMMs presented later in this 4 Mixture weights are not included for brevity.sCHAPTER 3. GENERALISED LINEAR GAUSSIAN MODELS 35 Factor Analysed Hidden... |

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Citation Context ...single set of parameters per phone but a linear time warping was used to normalise segment durations before the model was applied. Some gains compared to HMMs in phone classification task using TIMIT =-=[71]-=- corpus were reported. The application of LDSs for speech recognition has recently been addressed elsewhere [27, 28]. Most of the other segment models presented in the literature may be regarded as a ... |

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Citation Context ...lts for the 13 and 39-dimensional single and two observation noise component baseline FAHMMs on the 1200 utterance test set and 300 utterance train set. The best test set result in literature is 3.6% =-=[80]-=-. 90 xvsLIST OF TABLES xvi 7.7 The “oracle – idiot” word error rates for the 13 and 39-dimensional baseline FAHMMs. These give the limits for the word error rates that may be obtained by rescoring the... |

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Citation Context ...s been found that discriminative training yields better performance than ML. Discriminative optimisation criteria include maximum mutual information (MMI) [4], minimum classification error rate (MCE) =-=[63]-=-, frame discrimination [67] and minimum phone error rate [104] of which MMI and MPE have been the most successful in speech recognition [47, 126]. In comparison to ML training, the discriminative meth... |

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Citation Context ...sterior, ˜qn(m1), is found by matching the first two moments, E˜qn{m1} = E˜pn{m1} and E˜qn{m1m1} = E˜pn{m1m1}. This is also known as weak marginalisation and is the best approximation in the KL s=-=ense [72]. -=-It may be shown that the moment matching is equivalent to minimising the KL distance, D(˜pn(m1), ˜qn(m1)). The ADF can be summarised as algorithm 2. The exact formulae for the example may be found i... |

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Citation Context ...ar models [12]. In this work, the observation process is an important part of the correlation model for the high dimensional observation vectors. 3.2 Bayesian Networks In this work, Bayesian networks =-=[37, 94]-=- are used to illustrate the statistical independence assumptions between different random variables in probabilistic models. Bayesian networks are directed acyclic graphs, also known as graphical mode... |

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Maximum likelihood estimates of linear dynamic systems
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- 1965
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Citation Context ...tions and matrix algebra as described in Appendix E. Traditionally, the statistics of the smoothed state vector, p(xt|O) = N (xt; ˆxt, ˆ Σt), are obtained using the Rauch-Tung-Striebel (RTS) smooth=-=er [107, 108]. The RTS smoothing alg-=-orithm requires the above Kalman filter statistics be known. The recursion can be written as follows ˆΣt = Σt|t + Σt|tA ′ Σ −1 � � ˆΣt+1 −1 t+1|t − Σt+1|t Σt+1|tAΣt|t (3.39) ˆxt... |