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• W2911415034 abstract "Sparse residual tree (SRT) is an adaptive exploration method for multivariate scattered data approximation. It leads to sparse and stable approximations in areas where the data is sufficient or redundant, and points out the possible local regions where data refinement is needed. Sparse residual forest (SRF) is a combination of SRT predictors to further improve the approximation accuracy and stability according to the error characteristics of SRTs. The hierarchical parallel SRT algorithm is based on both tree decomposition and adaptive radial basis function (RBF) explorations, whereby for each child a sparse and proper RBF refinement is added to the approximation by minimizing the norm of the residual inherited from its parent. The convergence results are established for both SRTs and SRFs. The worst case time complexity of SRTs is $mathcal{O}(Nlog_2N)$ for the initial work and $mathcal{O}(log_2N)$ for each prediction, meanwhile, the worst case storage requirement is $mathcal{O}(Nlog_2N)$, where the $N$ data points can be arbitrary distributed. Numerical experiments are performed for several illustrative examples." @default.
• W2911415034 created "2019-02-21" @default.
• W2911415034 creator A5048723161 @default.
• W2911415034 creator A5075751135 @default.
• W2911415034 date "2019-02-18" @default.
• W2911415034 modified "2023-09-28" @default.
• W2911415034 title "Sparse residual tree and forest" @default.
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• W2911415034 doi "https://doi.org/10.48550/arxiv.1902.06443" @default.
• W2911415034 hasPublicationYear "2019" @default.
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