Geodesic
Power sum kernels in permutation learning
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 34, Tome 525 (2023), pp. 7-21
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper, we consider the use of power sum kernels in solving the problem of permutation learning. We present a way to approximate a symmetrized kernel that naturally arises in this problem using the Monte Carlo method and estimate the convergence rate. We also touch on the problem of partial rankings and present some results for the case when the number of fixed elements is 1 or 2. 
@article{ZNSL_2023_525_a1,
     author = {I. F. Azangulov and D. A. Eremeev},
     title = {Power sum kernels in permutation learning},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--21},
     year = {2023},
     volume = {525},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a1/}
}
TY  - JOUR
AU  - I. F. Azangulov
AU  - D. A. Eremeev
TI  - Power sum kernels in permutation learning
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2023
SP  - 7
EP  - 21
VL  - 525
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a1/
LA  - ru
ID  - ZNSL_2023_525_a1
ER  - 
%0 Journal Article
%A I. F. Azangulov
%A D. A. Eremeev
%T Power sum kernels in permutation learning
%J Zapiski Nauchnykh Seminarov POMI
%D 2023
%P 7-21
%V 525
%U http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a1/
%G ru
%F ZNSL_2023_525_a1
I. F. Azangulov; D. A. Eremeev. Power sum kernels in permutation learning. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 34, Tome 525 (2023), pp. 7-21. http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a1/

[1] M. Jerrum, A. Sinclair, E. Vigoda, “A polynomial-time approximation algorithms for permanent of a matrix with non-negative entries”, J. ACM, 51 (2004), 671–697

[2] R. Kondor, Group Theoretical Methods in Machine Learning, PhD Thesis, 2008

[3] R. Kondor, M. Barbosa, “Ranking with kernels in Fourier space”, COLT 2010 – The 23rd Conference on Learning Theory, 2010, 451–463

[4] I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford classic texts in the physical sciences, Clarendon Press, 1998

[5] C. E. Rasmussen, C. K. I. Williams, Gaussian Processes for Machine Learning, MIT Press, 2006

[6] H. J. Ryser, Combinatorial Mathematics, The Carus Mathematical Monographs, AMS, 1963

[7] V. N. Vapnik, The nature of statistical learning theory, Springer-Verlag, New York, 1995

[8] I. F. Azangulov, V. A. Borovitskii, A. V. Smolenskii, “Ob odnom klasse gaussovskikh protsessov na simmetricheskoi gruppe”, Zap. nauchn. semin. POMI, 515, 2022, 19–29