TY - JOUR

T1 - ON POWER SUM KERNELS ON SYMMETRIC GROUPS

AU - Azangulov, I.

AU - Borovitskiy, V.

AU - Smolensky, A.

N1 - Export Date: 03 March 2026; Cited By: 0; Correspondence Address: I. Azangulov; St.Petersburg State University, St.Peterburg, Russian Federation; email: iska.azn@gmail.com

PY - 2025

Y1 - 2025

N2 - In this note, we introduce a family of “power sum” kernels and the corresponding Gaussian processes on symmetric groups Sn. Such processes are bi-invariant: the action of Sn on itself from both sides does not change their finite-dimensional distributions. We show that the values of power sum kernels can be efficiently calculated, and we also propose a method enabling approximate sampling of the corresponding Gaussian processes with polynomial computational complexity. By doing this we provide the tools that are required to use the introduced family of kernels and the respective processes for statistical modeling and machine learning. Bibliography: 20 titles. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

AB - In this note, we introduce a family of “power sum” kernels and the corresponding Gaussian processes on symmetric groups Sn. Such processes are bi-invariant: the action of Sn on itself from both sides does not change their finite-dimensional distributions. We show that the values of power sum kernels can be efficiently calculated, and we also propose a method enabling approximate sampling of the corresponding Gaussian processes with polynomial computational complexity. By doing this we provide the tools that are required to use the introduced family of kernels and the respective processes for statistical modeling and machine learning. Bibliography: 20 titles. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

U2 - 10.1007/s10958-025-07976-x

DO - 10.1007/s10958-025-07976-x

M3 - статья

VL - 293

SP - 12

EP - 18

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -