# A Unifying Review of Linear Gaussian Models

@article{Roweis1999AUR, title={A Unifying Review of Linear Gaussian Models}, author={Sam T. Roweis and Zoubin Ghahramani}, journal={Neural Computation}, year={1999}, volume={11}, pages={305-345} }

Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, 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…

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## References

SHOWING 1-10 OF 119 REFERENCES

Resolution-Based Complexity Control for Gaussian Mixture Models

- Computer ScienceNeural Computation
- 2001

This work presents a complexity control scheme, which provides an effective means for avoiding the problem of overfitting usually encountered with unconstrained (mixtures of) gaussians in high dimensions within a common deterministic annealing framework.

Variational Learning for Switching State-Space Models

- Computer ScienceNeural Computation
- 2000

A new statistical model for time series that iteratively segments data into regimes with approximately linear dynamics and learns the parameters of each of these linear regimes is introduced and the results suggest that variational approximations are a viable method for inference and learning in switching state-space models.

Mixtures of Probabilistic Principal Component Analyzers

- Computer ScienceNeural Computation
- 1999

PCA is formulated within a maximum likelihood framework, based on a specific form of gaussian latent variable model, which leads to a well-defined mixture model for probabilistic principal component analyzers, whose parameters can be determined using an expectation-maximization algorithm.

Switching State-Space Models

- Computer Science
- 1996

A statistical model for times series data with nonlinear dynamics which iteratively segments the data into regimes with approximately linear dynamics and learns the parameters of each of those regimes, and presents a variational approximation which maximizes a lower bound on the log likelihood.

Probabilistic Independence Networks for Hidden Markov Probability Models

- Computer ScienceNeural Computation
- 1997

It is shown that the well-known forward-backward and Viterbi algorithms for HMMs are special cases of more general inference algorithms for arbitrary PINs and the existence of inference and estimation algorithms for more general graphical models provides a set of analysis tools for HMM practitioners who wish to explore a richer class of HMM structures.

Blind source separation and deconvolution: the dynamic component analysis algorithm

- Computer Science
- 1998

We derive a novel family of unsupervised learning algorithms for blind separation of mixed and convolved sources. Our approach is based on formulating the separation problem as a learning task of a…

Modeling Acoustic Correlations by Factor Analysis

- Computer ScienceNIPS
- 1997

This work evaluates the combined use of mixture densities and factor analysis in HMMs that recognize alphanumeric strings and finds that these methods, properly combined, yield better models than either method on its own.

Parameter estimation for linear dynamical systems

- Computer Science, Mathematics
- 1996

The Expectation Maximization (EM) algorithm for estimating the parameters of linear systems (LDS) is introduced and its relation to factor analysis and other data modeling techniques is pointed out.

Regression with Input-dependent Noise: A Gaussian Process Treatment

- Mathematics, Computer ScienceNIPS
- 1997

This paper shows that prior uncertainty about the parameters controlling both processes can be handled and that the posterior distribution of the noise rate can be sampled from using Markov chain Monte Carlo methods and gives a posterior noise variance that well-approximates the true variance.

Maximum Likelihood and Covariant Algorithms for Independent Component Analysis

- Computer Science
- 1996

It is shown that Bell and Sejnowski’s (1995) algorithm can be viewed as a maximum likelihood algorithm for the optimization of a linear generative model and a covariant version of the algorithm is derived.