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A forward-backward greedy approach for sparse multiscale learning
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DOI：10.1016/j.cma.2022.115420.png)
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摘要
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Multiscale models are known to be successful in uncovering and representing structure in data at different resolutions. We propose here a feature driven Reproducing Kernel Hilbert Space (RKHS) for which the associated kernel has a weighted multiscale structure. For generating approximations in this space, we provide a practical forward-backward algorithm that is shown to greedily construct a set of basis functions having a multiscale structure which enables sparse efficient representation of the given data and efficient predictions. We provide a detailed analysis of the algorithm including recommendations for selecting algorithmic hyperparameters and estimating probabilistic rates of convergence at individual scales. We also extend this analysis to a multiscale setting, studying the effects of finite scale truncation and quality of solution in the inherent RKHS. In the last section, we analyze the performance of the approach on a variety of simulations and real data sets illustrating the efficiency claims in terms of model quality and data reduction.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keyword:
Multiscale models
Greedy algorithms
Sparse representation
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7.3
论文数:
1.3W
被引数:
5.6W
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