程序代写代做代考 data mining flex Data Mining and Machine Learning

Data Mining and Machine Learning
HMMs for Automatic Speech Recognition: Types of HMMs
Peter Jančovič Slide 1
Data Mining and Machine Learning

Objectives To understand
 Differences between types of HMMs
Slide 2
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HMM taxonomy
General HMMs
Conventional HMMs
HMM / NN ‘Hybrids’ Best of both Worlds?
Hidden semi-Markov models Improved duration modelling
Segmental HMMs
Improved segment modelling
Slide 3
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Types of Conventional HMM
Conventional HMMs
Continuous HMMs
Non-Gaussian Continuous HMMs
Gaussian HMMs
Gaussian Mixture HMMs
Slide 4
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Discrete HMMs

Front-End Processing Re-Visited
Vectors in d-dimensional (continuous) space
Vectors in d-dimensional (continuous) space
Symbols from a finite set
Linear Transform e.g. cosine transform
Vector Quantisation
Speech Recognition
Slide 5
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Front-end Processing e.g. filterbank analysis

Discrete HMMs
 If VQ is used, then a state output PDF bi is defined by a list of probabilities
bi(m)=Prob(yt=zm|xt =si)
 The resulting HMM is a discrete HMM
 Common in mid-1980/ early-1990s
 Computational advantages
 Disadvantages
– VQ may introduce non-recoverable errors
– Choice of metric d for VQ?
 Outperformed by Continuous HMM
Slide 6
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Continuous HMMs
 Without VQ, bi (y) must be defined for any y in the
(continuous) observation set S
 Hence discrete state output PDFs no longer viable
 Use parametric continuous state output PDFs – Continuous HMMs
 Choice of PDF restricted by mathematical tractability and computational usefulness (see “HMM training & recognition” later)
 Most people begin with Gaussian PDFs
 Resulting HMMs called Gaussian HMMs
Slide 7
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Gaussian HMMs
 State output PDFs are multivariate Gaussian
11 b(y) exp  ymC1ym
i (2)dC 2 i i i i
 mi and Ci are the mean vector and covariance matrix which define bi
Slide 8
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Gaussian HMMs – Issues
 Significant computational savings if covariance matrix can be assumed to be diagonal
 In general, Gaussian PDFs are not flexible enough to model speech pattern variability accurately
– In many applications (e.g. modelling speech from multiple speakers) a unimodal PDF is inadequate
– Even if unimodal PDF is basically OK there may be more subtle inadequacies
Slide 9
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Gaussian Mixture HMMs
 Any PDF can be approximated arbitrarily closely by a Gaussian mixture PDF with sufficient components
 But…
– More mixture components require more data for
robust model parameter estimation
– Parameter smoothing and sharing needed (e.g. ‘tied mixtures’, ‘grand variance’,…)
 Gaussian mixture HMMs widely used in systems in research laboratories
Slide 10
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Relationship with Neural Networks
 ‘Classical’ HMM training methods focus on fitting state output PDFs to data (modelling), rather than minimizing overlap between PDFs (discrimination)
 NNs are good at discrimination
 But ‘classical’ NNs poor at coping with time-
varying data
 Research interest in ‘hybrid’ systems which use NNs to relate the observations to the states of the underlying Markov model
 More recently, recurrent NNs also replacing HMMs
Slide 11
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Summary
 Types of HMM
– Discrete HMMs
– Continuous HMMs – Gaussian Mixture HMMs
Slide 12
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