Regularization theory and neural networks architectures
Neural Computation
Data mining with sparse grids using simplicial basis functions
Proceedings of the seventh ACM SIGKDD international conference on Knowledge discovery and data mining
Computing
Spatially adaptive sparse grids for high-dimensional data-driven problems
Journal of Complexity
Classification with sums of separable functions
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part I
A Finite Element Method for Density Estimation with Gaussian Process Priors
SIAM Journal on Numerical Analysis
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We consider the sparse grid combination technique for regression, which we regard as a problem of function reconstruction in some given function space. We use a regularised least squares approach, discretised by sparse grids and solved using the so-called combination technique, where a certain sequence of conventional grids is employed. The sparse grid solution is then obtained by addition of the partial solutions with combination co-efficients dependent on the involved grids. This approach shows instabilities in certain situations and is not guaranteed to converge with higher discretisation levels. In this article we apply the recently introduced optimised combination technique, which repairs these instabilities. Now the combination coefficients also depend on the function to be reconstructed, resulting in a non-linear approximation method which achieves very competitive results. We show that the computational complexity of the improved method still scales only linear in regard to the number of data.