GENERALISED LINEAR GAUSSIAN MODELS
A-V.I. Rosti & M.J.F. Gales
November 2001
This paper addresses the time-series modelling of high dimensional data. Current ly, the hidden Markov model (HMM) is the most popular and successful model espec ially in speech recognition. However, there are well known shortcomings in HMMs particularly in the modelling of the correlation between successive observation vectors; that is, inter-frame correlation. Standard diagonal covariance matrix H MMs also lack the modelling of the spatial correlation in the feature vectors; t hat is, intra-frame correlation. Several other time-series models have been prop osed recently especially in the segment model framework to address the inter-fra me correlation problem such as Gauss-Markov and dynamical system segment models. The lack of intra-frame correlation has been compensated for with transform sch emes such as semi-tied full covariance matrices (STC). All these models can be r egarded as belonging to the broad class of generalised linear Gaussian models. L inear Gaussian models (LGM) are popular as many forms may be trained efficiently using the expectation maximisation algorithm. In this paper, several LGMs and g eneralised LGMs are reviewed. The models can be roughly categorised into four co mbinations according to two different state evolution and two different observat ion processes. The state evolution process can be based on a discrete finite sta te machine such as in the HMMs or a linear first-order Gauss-Markov process such as in the traditional linear dynamical systems. The observation process can be represented as a factor analysis model or a linear discriminant analysis model. General HMMs and schemes proposed to improve their performance such as STC can b e regarded as special cases in this framework.
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