Hierarchical Gaussian process latent variable models

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.

[1]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[2]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[3]  D. Mackay,et al.  Bayesian neural networks and density networks , 1995 .

[4]  Christopher M. Bishop,et al.  GTM: The Generative Topographic Mapping , 1998, Neural Computation.

[5]  D. Mackay,et al.  Introduction to Gaussian processes , 1998 .

[6]  Christopher M. Bishop,et al.  A Hierarchical Latent Variable Model for Data Visualization , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Christopher K. I. Williams,et al.  Tree-structured belief networks as models of images , 1999 .

[8]  Michael E. Tipping,et al.  Probabilistic Principal Component Analysis , 1999 .

[9]  Daniel P. Huttenlocher,et al.  Efficient matching of pictorial structures , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[10]  David A. Forsyth,et al.  Mixtures of trees for object recognition , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[11]  Christopher K. I. Williams,et al.  Combining Belief Networks and Neural Networks for Scene Segmentation , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Peter Tiño,et al.  Hierarchical GTM: Constructing Localized Nonlinear Projection Manifolds in a Principled Way , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  David A. Forsyth,et al.  Finding and tracking people from the bottom up , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[14]  Aaron Hertzmann,et al.  Style-based inverse kinematics , 2004, ACM Trans. Graph..

[15]  Sidharth Bhatia,et al.  Tracking loose-limbed people , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[16]  David J. Fleet,et al.  Priors for people tracking from small training sets , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[17]  David J. Fleet,et al.  Gaussian Process Dynamical Models , 2005, NIPS.

[18]  Neil D. Lawrence,et al.  Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models , 2005, J. Mach. Learn. Res..

[19]  Daniel P. Huttenlocher,et al.  Beyond trees: common-factor models for 2D human pose recovery , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[20]  Joaquin Quiñonero Candela,et al.  Local distance preservation in the GP-LVM through back constraints , 2006, ICML.

[21]  David J. Fleet,et al.  3D People Tracking with Gaussian Process Dynamical Models , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[22]  Balaraman Ravindran,et al.  Image Modeling Using Tree Structured Conditional Random Fields , 2007, IJCAI.

[23]  Neil D. Lawrence,et al.  WiFi-SLAM Using Gaussian Process Latent Variable Models , 2007, IJCAI.

[24]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[25]  M. Gusarova,et al.  Nuclear Instruments and Methods in Physics Research , 2009 .