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🔗 Source: cea.hal.science
📊 Size: 6.18 MB
👤 Author: Gabriel Sarazin, Amandine Marrel, Sébastien da Veiga, Vincent Chabridon
⬇️ Downloads: 131

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The paper "What is hidden behind the Sobolev kernels involved in the HSIC-ANOVA decomposition?" by Gabriel Sarazin, Amandine Marrel, Sébastien da Veiga, and Vincent Chabridon explores the properties of Sobolev kernels used in the Hilbert-Schmidt Independence Criterion (HSIC) decomposition. The authors demonstrate that Sobolev kernels are characteristic, ensuring the nullity of Sobolev-based HSIC indices is equivalent to independence. They also identify an explicit feature map for Sobolev kernels, which can help understand the spectrum of dependency patterns captured by this novel HSIC index. The feature map is obtained through Mercer's theorem and is used to tackle the eigenvalue problem arising from it. The authors investigate the benefits of kernel feature analysis and demonstrate that the eigenvalue problem is equivalent to a Cauchy problem, which is solved analytically for r = 1 and approximately for r = 2. The results provide new insights into Sobolev kernels and their use in HSIC-ANOVA decomposition for global sensitivity analysis.

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The paper "What is hidden behind the Sobolev kernels involved in the HSIC-ANOVA decomposition?" by Gabriel Sarazin, Amandine Marrel, Sébastien da Veiga, and...

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  • File Format: PDF
  • File Size: 6.18 MB
  • Pages: 14
  • Language: EN
  • Author: Gabriel Sarazin, Amandine Marrel, Sébastien da Veiga, Vincent Chabridon
  • Total Downloads: 131
  • Last Updated: 2 months ago

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