Accurate Downdating of Least Squares Solutions
SIAM Journal on Matrix Analysis and Applications
Sparse on-line Gaussian processes
Neural Computation
Compactly Supported RBF Kernels for Sparsifying the Gram Matrix in LS-SVM Regression Models
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
Support Vector Regression and Classification Based Multi-View Face Detection and Recognition
FG '00 Proceedings of the Fourth IEEE International Conference on Automatic Face and Gesture Recognition 2000
Model-Based Head Pose Tracking With Stereovision
FGR '02 Proceedings of the Fifth IEEE International Conference on Automatic Face and Gesture Recognition
A column approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Sparse Bayesian Learning for Efficient Visual Tracking
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sparse and Semi-supervised Visual Mapping with the S^3GP
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Incremental Learning for Robust Visual Tracking
International Journal of Computer Vision
Fast incremental square root information smoothing
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Multivariate relevance vector machines for tracking
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
Recognition of human head orientation based on artificial neural networks
IEEE Transactions on Neural Networks
Supporting user-defined functions on uncertain data
Proceedings of the VLDB Endowment
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We present a new Gaussian Process inference algorithm, called Online Sparse Matrix Gaussian Processes (OSMGP), and demonstrate its merits with a few vision applications. The OSMGP is based on the observation that for kernels with local support, the Gram matrix is typically sparse. Maintaining and updating the sparse Cholesky factor of the Gram matrix can be done efficiently using Givens rotations. This leads to an exact, online algorithm whose update time scales linearly with the size of the Gram matrix. Further, if approximate updates are permissible, the Cholesky factor can be maintained at a constant size using hyperbolic rotations to remove certain rows and columns corresponding to discarded training examples. We demonstrate that, using these matrix downdates, online hyperparameter estimation can be included without affecting the linear runtime complexity of the algorithm. The OSMGP algorithm is applied to head-pose estimation and visual tracking problems. Experimental results demonstrate that the proposed method is accurate, efficient and generalizes well using online learning.