Iterative methods for solving linear systems
Iterative methods for solving linear systems
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
A Unifying View of Sparse Approximate Gaussian Process Regression
The Journal of Machine Learning Research
| Hi-index | 0.00 |
To compute the exact solution of Gaussian process regression one needs $\mathcal{O}(N^3)$ computations for direct and $\mathcal{O}(N^2)$ for iterative methods since it involves a densely populated kernel matrix of size N×N, here Ndenotes the number of data. This makes large scale learning problems intractable by standard techniques.We propose to use an alternative approach: the kernel matrix is replaced by a data-sparse approximation, called an ${\mathcal H}^2$-matrix. This matrix can be represented by only ${\cal O}(N m)$ units of storage, where mis a parameter controlling the accuracy of the approximation, while the computation of the ${\mathcal H}^2$-matrix scales with ${\cal O}(N m \log N)$.Practical experiments demonstrate that our scheme leads to significant reductions in storage requirements and computing times for large data sets in lower dimensional spaces.