ArticleJournal of multivariate analysis2024
Nonlinear sufficient dimension reduction for distribution-on-distribution regression.
Article in Journal of multivariate analysis, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
What it found
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Who cites it
3 citing papers in PubMed.
- NONLINEAR GLOBAL FRÉCHET REGRESSION FOR RANDOM OBJECTS VIA WEAK CONDITIONAL EXPECTATION.Annals of statistics · 2025Article
- Sparse kernel sufficient dimension reduction.Journal of nonparametric statistics · 2024Article
- Dimension Reduction for Fréchet Regression.Journal of the American Statistical Association · 2024Article
Corrections and comments
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Authors and funding
3 authors.
Funding
Abstract
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.
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Registered trials
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