Nonlinear sufficient dimension reduction for distribution-on-distribution regression.
Nonlinear sufficient dimension reduction for distribution-on-distribution regression.
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DOI：
10.1016/j.jmva.2024.105302
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发表时间：
2022-07
影响因子：
1.6
通讯作者：
Q. Zhang;Bing Li;Lingzhou Xue
中科院分区：
文献类型：
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作者：
Q. Zhang;Bing Li;Lingzhou Xue
我们引入了一种新的非线性充分降维方法，在这种情况下，预测器和响应都是分布数据，建模为度量空间的成员。我们的关键步骤是在度量空间上构建通用核（cc-universal），这导致为预测器和响应再现核希尔伯特空间，这些空间足够丰富，可以表征决定足够降维的条件独立性。对于单变量分布，我们使用Wasserstein距离构造通用核，而对于多变量分布，我们采用切片Wasserstein距离。切片的Wasserstein距离确保度量空间具有与Wasserstein空间相似的拓扑性质，同时也提供了显著的计算优势。基于综合数据的数值计算结果表明，该方法优于可能的竞争方法。该方法还适用于几个数据集，包括生育率和死亡率数据和卡尔加里温度数据。
We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels (cc-universal) on the metric spaces, which results in reproducing kernel Hilbert spaces for the predictor and response that are rich enough to characterize the conditional independence that determines sufficient dimension reduction. For univariate distributions, we construct the universal kernel using the Wasserstein distance, while for multivariate distributions, we resort to the sliced Wasserstein distance. The sliced Wasserstein distance ensures that the metric space possesses similar topological properties to the Wasserstein space, while also offering significant computation benefits. Numerical results based on synthetic data show that our method outperforms possible competing methods. The method is also applied to several data sets, including fertility and mortality data and Calgary temperature data.