Geodesic
On power-sum kernels on symmetric groups
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 33, Tome 515 (2022), pp. 19-29

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In this note, we introduce a family of “power-sum” covariance functions and the corresponding Gaussian processes on symmetric groups $S_n$. Such processes are bi-invariant: the action of $S_n$ on itself from both sides does not change their finite-dimensional distributions. We show that the values of power-sum covariance functions can be efficiently calculated, and we also propose a method enabling approximate modeling of the corresponding processes with polynomial computational complexity. By doing this we provide the tools that are required to use the introduced family of processes for statistical modeling. 
@article{ZNSL_2022_515_a1,
     author = {I. Azangulov and V. A. Borovitskiy and A. V. Smolensky},
     title = {On power-sum kernels on symmetric groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {19--29},
     publisher = {mathdoc},
     volume = {515},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a1/}
}
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I. Azangulov; V. A. Borovitskiy; A. V. Smolensky. On power-sum kernels on symmetric groups. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 33, Tome 515 (2022), pp. 19-29. http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a1/