Learning for Larger Datasets with the Gaussian Process Latent Variable Model

In this paper we apply the latest techniques in sparse Gaussian process regression (GPR) to the Gaussian process latent variable model (GPLVM). We review three techniques and discuss how they may be implemented in the context of the GP-LVM. Each approach is then implemented on a well known benchmark data set and compared with earlier attempts to sparsify the model.

[1]  F. Girosi,et al.  Networks for approximation and learning , 1990, Proc. IEEE.

[2]  Michael I. Jordan,et al.  Advances in Neural Information Processing Systems 30 , 1995 .

[3]  C. Bishop,et al.  Analysis of multiphase flows using dual-energy gamma densitometry and neural networks , 1993 .

[4]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

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

[6]  G. Wahba,et al.  Hybrid Adaptive Splines , 1997 .

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

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

[9]  Volker Tresp,et al.  A Bayesian Committee Machine , 2000, Neural Computation.

[10]  Alexander J. Smola,et al.  Sparse Greedy Gaussian Process Regression , 2000, NIPS.

[11]  Christopher K. I. Williams,et al.  Using the Nyström Method to Speed Up Kernel Machines , 2000, NIPS.

[12]  Lehel Csató,et al.  Sparse On-Line Gaussian Processes , 2002, Neural Computation.

[13]  Carl Edward Rasmussen,et al.  Observations on the Nyström Method for Gaussian Process Prediction , 2002 .

[14]  Anton Schwaighofer,et al.  Transductive and Inductive Methods for Approximate Gaussian Process Regression , 2002, NIPS.

[15]  Neil D. Lawrence,et al.  Fast Sparse Gaussian Process Methods: The Informative Vector Machine , 2002, NIPS.

[16]  Neil D. Lawrence,et al.  Fast Forward Selection to Speed Up Sparse Gaussian Process Regression , 2003, AISTATS.

[17]  Aaron Hertzmann,et al.  Style-based inverse kinematics , 2004, SIGGRAPH 2004.

[18]  Carl E. Rasmussen,et al.  A Unifying View of Sparse Approximate Gaussian Process Regression , 2005, J. Mach. Learn. Res..

[19]  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.

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

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

[22]  Zoubin Ghahramani,et al.  Sparse Gaussian Processes using Pseudo-inputs , 2005, NIPS.

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

[24]  Geoffrey E. Hinton,et al.  Modeling Human Motion Using Binary Latent Variables , 2006, NIPS.

[25]  Neil D. Lawrence Large Scale Learning with the Gaussian Process Latent Variable Model , 2008 .

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

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