# Hierarchical Gaussian Process Latent Variable Models

Neil D. Lawrence, University of Sheffield
Andrew J. Moore

in Proceedings of the International Conference in Machine Learning 24, pp 481-488

#### Abstract

The Gaussian process latent variable model (GP-LVM) is a powerful approach for probabilistic modelling of high dimensional data through dimensional reduction. In this paper we extend the GP-LVM through hierarchies. A hierarchical model (such as a tree) allows us to express conditional independencies in the data as well as the manifold structure. We first introduce Gaussian process hierarchies through a simple dynamical model, we then extend the approach to a more complex hierarchy which is applied to the visualisation of human motion data sets.

  @InProceedings{lawrence-hgplvm07, title = {Hierarchical Gaussian Process Latent Variable Models}, author = {Neil D. Lawrence and Andrew J. Moore}, booktitle = {Proceedings of the International Conference in Machine Learning}, pages = {481}, year = {2007}, editor = {Zoubin Ghahramani}, volume = {24}, month = {00}, publisher = {Omnipress}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2007-01-01-lawrence-hgplvm07.md}, url = {http://inverseprobability.com/publications/lawrence-hgplvm07.html}, abstract = {The Gaussian process latent variable model (GP-LVM) is a powerful approach for probabilistic modelling of high dimensional data through dimensional reduction. In this paper we extend the GP-LVM through hierarchies. A hierarchical model (such as a tree) allows us to express conditional independencies in the data as well as the manifold structure. We first introduce Gaussian process hierarchies through a simple dynamical model, we then extend the approach to a more complex hierarchy which is applied to the visualisation of human motion data sets.}, crossref = {Ghahramani:icml07}, key = {Lawrence:hgplvm07}, linkpdf = {ftp://ftp.dcs.shef.ac.uk/home/neil/hgplvm.pdf}, linksoftware = {https://github.com/SheffieldML/hgplvm/}, group = {manml,gp,gplvm,dimensional reduction} }
 %T Hierarchical Gaussian Process Latent Variable Models %A Neil D. Lawrence and Andrew J. Moore %B %C Proceedings of the International Conference in Machine Learning %D %E Zoubin Ghahramani %F lawrence-hgplvm07 %I Omnipress %P 481--488 %R %U http://inverseprobability.com/publications/lawrence-hgplvm07.html %V 24 %X The Gaussian process latent variable model (GP-LVM) is a powerful approach for probabilistic modelling of high dimensional data through dimensional reduction. In this paper we extend the GP-LVM through hierarchies. A hierarchical model (such as a tree) allows us to express conditional independencies in the data as well as the manifold structure. We first introduce Gaussian process hierarchies through a simple dynamical model, we then extend the approach to a more complex hierarchy which is applied to the visualisation of human motion data sets. 
 TY - CPAPER TI - Hierarchical Gaussian Process Latent Variable Models AU - Neil D. Lawrence AU - Andrew J. Moore BT - Proceedings of the International Conference in Machine Learning PY - 2007/01/01 DA - 2007/01/01 ED - Zoubin Ghahramani ID - lawrence-hgplvm07 PB - Omnipress SP - 481 EP - 488 L1 - ftp://ftp.dcs.shef.ac.uk/home/neil/hgplvm.pdf UR - http://inverseprobability.com/publications/lawrence-hgplvm07.html AB - The Gaussian process latent variable model (GP-LVM) is a powerful approach for probabilistic modelling of high dimensional data through dimensional reduction. In this paper we extend the GP-LVM through hierarchies. A hierarchical model (such as a tree) allows us to express conditional independencies in the data as well as the manifold structure. We first introduce Gaussian process hierarchies through a simple dynamical model, we then extend the approach to a more complex hierarchy which is applied to the visualisation of human motion data sets. ER - 
 Lawrence, N.D. & Moore, A.J.. (2007). Hierarchical Gaussian Process Latent Variable Models. Proceedings of the International Conference in Machine Learning 24:481-488