2026-10-13T09:50:38Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33893343 2026-09-17T13:11:54Z category_4 category_7 category_13 category_15 category_19 category_21 category_811 category_133 portal_87 item_type_3 month_year_09_2026

Nonparametric Feature Screening for Non-Euclidean Data Moshu Xu (25024422) Leheng Cai (18804937) Qirui Hu (2953989) Xu Guo (174019) Biochemistry Medicine Genetics Neuroscience Pharmacology Biotechnology Mathematical Sciences not elsewhere classified Plant Biology Feature screening Local Fréchet regression Non-Euclidean data Nonlinearity <p>In this paper, we consider the feature screening problem when the responses take values in non-Euclidean spaces and the inherent structure is nonlinear. We first revisit the concept of the Fréchet R⊕2 and prove that it possesses important properties analogous to those of the classical R2, including existence, boundedness, goodness of fit, monotonicity, and scale invariance. Building on these properties, we develop a novel feature screening procedure, termed local Fréchet sure independence screening, which identifies important covariates by evaluating the empirical Fréchet R⊕2 from corresponding univariate local Fréchet regressions. Under mild conditions, we establish the uniform consistency, sure screening, and sure ranking properties of the proposed procedure. Extensive numerical studies provide strong empirical support for the correctness and effectiveness of our methodology. Two representative non-Euclidean datasets, mortality data and FC Barcelona match data, with distribution-valued and matrix-valued responses, respectively, are used to illustrate the practical performance of our method.</p> 2026-09-17T13:11:54Z Dataset Dataset 10.6084/m9.figshare.33893343.v1 https://figshare.com/articles/dataset/Nonparametric_Feature_Screening_for_Non-Euclidean_Data/33893343 CC BY 4.0