# Variational Gaussian Process Dynamical Systems

Andreas Damianou, University of Sheffield
Michalis K. Titsias, University of Athens
Neil D. Lawrence, University of Sheffield

in Advances in Neural Information Processing Systems 24

#### Abstract

High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear probabilistic approaches to this data are required. In this paper we introduce the variational Gaussian process dynamical system. Our work builds on recent variational approximations for Gaussian process latent variable models to allow for nonlinear dimensionality reduction simultaneously with learning a dynamical prior in the latent space. The approach also allows for the appropriate dimensionality of the latent space to be automatically determined. We demonstrate the model on a human motion capture data set and a series of high resolution video sequences.

  @InProceedings{damianou-vgpds11, title = {Variational Gaussian Process Dynamical Systems}, author = {Andreas Damianou and Michalis K. Titsias and Neil D. Lawrence}, booktitle = {Advances in Neural Information Processing Systems}, year = {2011}, editor = {Peter Bartlett and Fernando Peirrera and Christopher K. I. Williams and John Lafferty}, volume = {24}, address = {Cambridge, MA}, month = {00}, publisher = {MIT Press}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2011-01-01-damianou-vgpds11.md}, url = {http://inverseprobability.com/publications/damianou-vgpds11.html}, abstract = {High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear probabilistic approaches to this data are required. In this paper we introduce the variational Gaussian process dynamical system. Our work builds on recent variational approximations for Gaussian process latent variable models to allow for nonlinear dimensionality reduction simultaneously with learning a dynamical prior in the latent space. The approach also allows for the appropriate dimensionality of the latent space to be automatically determined. We demonstrate the model on a human motion capture data set and a series of high resolution video sequences.}, crossref = {Bartlett:nips11}, key = {Damianou:vgpds11}, linkpdf = {ftp://ftp.dcs.shef.ac.uk/home/neil/VGPDS_Nips11.pdf}, linksoftware = {https://github.com/SheffieldML/vargplvm}, OPTgroup = {} }
 %T Variational Gaussian Process Dynamical Systems %A Andreas Damianou and Michalis K. Titsias and Neil D. Lawrence %B %C Advances in Neural Information Processing Systems %D %E Peter Bartlett and Fernando Peirrera and Christopher K. I. Williams and John Lafferty %F damianou-vgpds11 %I MIT Press %P -- %R %U http://inverseprobability.com/publications/damianou-vgpds11.html %V 24 %X High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear probabilistic approaches to this data are required. In this paper we introduce the variational Gaussian process dynamical system. Our work builds on recent variational approximations for Gaussian process latent variable models to allow for nonlinear dimensionality reduction simultaneously with learning a dynamical prior in the latent space. The approach also allows for the appropriate dimensionality of the latent space to be automatically determined. We demonstrate the model on a human motion capture data set and a series of high resolution video sequences. 
 TY - CPAPER TI - Variational Gaussian Process Dynamical Systems AU - Andreas Damianou AU - Michalis K. Titsias AU - Neil D. Lawrence BT - Advances in Neural Information Processing Systems PY - 2011/01/01 DA - 2011/01/01 ED - Peter Bartlett ED - Fernando Peirrera ED - Christopher K. I. Williams ED - John Lafferty ID - damianou-vgpds11 PB - MIT Press SP - EP - L1 - ftp://ftp.dcs.shef.ac.uk/home/neil/VGPDS_Nips11.pdf UR - http://inverseprobability.com/publications/damianou-vgpds11.html AB - High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear probabilistic approaches to this data are required. In this paper we introduce the variational Gaussian process dynamical system. Our work builds on recent variational approximations for Gaussian process latent variable models to allow for nonlinear dimensionality reduction simultaneously with learning a dynamical prior in the latent space. The approach also allows for the appropriate dimensionality of the latent space to be automatically determined. We demonstrate the model on a human motion capture data set and a series of high resolution video sequences. ER - 
 Damianou, A., Titsias, M.K. & Lawrence, N.D.. (2011). Variational Gaussian Process Dynamical Systems. Advances in Neural Information Processing Systems 24:-