| Abstract: |
| This paper proposes a kernel variable importance measure (KvIM) based on the maximum mean
discrepancy (MMD). KvIM can effectively measure the importance of an individual dimension in
contributing to the distributional difference by constructing weighted MMD and applying perturbations
to evaluate MMD changes through assigned weights. It has advantages such as non-parametric,
model-free, comprehensive consideration of the dependencies among dimensions, and suitability for
high-dimensional data. Furthermore, the consistency of empirical KvIM under general conditions
and its theoretical properties in high-dimensional settings were studied. In addition, we also apply
KvIM to classification problems and streaming datasets and propose a KvIM-enhanced classification
approach and renewable empirical KvIM accordingly. Numerous numerical studies illustrate that
the proposed method is feasible and effective. |
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