Online sparse Gaussian process regression and its applications.

We present a new Gaussian process (GP) inference algorithm, called online sparse matrix Gaussian processes (OSMGP), and demonstrate its merits by applying it to the problems of head pose estimation and visual tracking. The OSMGP is based upon 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, we provide a method for constant time operation of the OSMGP using matrix downdates. The downdates maintain the Cholesky factor at a constant size by removing certain rows and columns corresponding to discarded training examples. We demonstrate that, using these matrix downdates, online hyperparameter estimation can be included at cost linear in the number of total training examples. We describe a robust appearance-based head pose estimation system based upon the OSMGP. Numerous experiments and comparisons with existing methods using a large dataset system demonstrate the efficiency and accuracy of our system. Further, to showcase the applicability of OSMGP to a wide variety of problems, we also describe a regression-based visual tracking method. Experiments show that our OSMGP algorithm generalizes well using online learning.