BibTeX
@MISC{n.n._thecontinuous,
author = {n.n.},
title = {The continuous latent variable modelling },
year = {}
}
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Abstract
formalism This chapter gives the theoretical basis for continuous latent variable models. Section 2.1 defines intuitively the concept of latent variable models and gives a brief historical introduction to them. Section 2.2 uses a simple example, inspired by the mechanics of a mobile point, to justify and explain latent variables. Section 2.3 gives a more rigorous definition, which we will use throughout this thesis. Section 2.6 describes the most important specific continuous latent variable models and section 2.7 defines mixtures of continuous latent variable models. The chapter discusses other important topics, including parameter estimation, identifiability, interpretability and marginalisation in high dimensions. Section 2.9 on dimensionality reduction will be the basis for part II of the thesis. Section 2.10 very briefly mentions some applications of continuous latent variable models for dimensionality reduction. Section 2.11 shows a worked example of a simple continuous latent variable model. Section 2.12 give some complementary mathematical results, in particular the derivation of a diagonal noise GTM model and of its EM algorithm. 2.1 Introduction and historical overview of latent variable models Latent variable models are probabilistic models that try to explain a (relatively) high-dimensional process in
Keyphrases
continuous latent variable model dimensionality reduction parameter estimation simple continuous latent variable model complementary mathematical result theoretical basis latent variable model defines mixture mobile point diagonal noise gtm model continuous latent simple example briefly mention historical overview rigorous definition latent variable em algorithm important topic high-dimensional process probabilistic model brief historical introduction high dimension worked example part ii
