Permutation invariant functions: statistical tests, dimension reduction in metric entropy and estimation

arXiv:2403.01671v1 Announce Type: new
Abstract: Permutation invariance is among the most common symmetry that can be exploited to simplify complex problems in machine learning (ML). There has been a tremendous surge of research activities in building permutation invariant ML architectures. However, less attention is given to how to statistically test for permutation invariance of variables in a multivariate probability distribution where the dimension is allowed to grow with the sample size. Also, in terms of a statistical theory, little is …

abstract architectures arxiv attention building cs.lg entropy functions machine machine learning research statistical symmetry tests type