A Unifying Review of Linear Gaussian Models

Sam Roweis and Zoubin Ghahramani

Gatsby Computational Neuroscience Unit
University College London
London, WC1N 3AR, UK

Factor analysis, principal component analysis (PCA), mixtures of Gaussian clusters, vector quantization (VQ), Kalman filter models and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities we show how independent component analysis (ICA) is also a variation of the same basic generative model. We show that factor analysis and mixtures of Gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data known as sensible principal component analysis (SPCA) as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudo-code for inference and learning for all the basic models.

Neural Computation 11(2):305--345 (1999) postscript.

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