  Model selection is critical in the modern statistics and machine learning
community. However, most existing works do not apply to heavy-tailed data,
which are commonly encountered in real applications, such as the single-cell
multiomics data. In this paper, we propose a rank-sum based approach that
outputs a confidence set containing the optimal model with guaranteed
probability. Motivated by conformal inference, we developed a general method
that is applicable without moment or tail assumptions on the data. We
demonstrate the advantage of the proposed method through extensive simulation
and a real application on the COVID-19 genomics dataset (Stephenson et al.,
2021). To perform the inference on rank-sum statistics, we derive a general
Gaussian approximation theory for high dimensional two-sample U-statistics,
which may be of independent interest to the statistics and machine learning
community.
