TY - GEN
T1 - On power-law kernels, corresponding Reproducing Kernel Hilbert Space and applications
AU - Ghoshdastidar, Debarghya
AU - Dukkipati, Ambedkar
PY - 2013
Y1 - 2013
N2 - The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We propose two power-law kernels by generalizing Gaussian and Laplacian kernels. This generalization is based on distributions, arising out of maximization of a generalized information measure known as nonextensive entropy that is very well studied in statistical mechanics.We prove that the proposed kernels are positive definite, and provide some insights regarding the corresponding Reproducing Kernel Hilbert Space (RKHS). We also study practical significance of both kernels in classification and regression, and present some simulation results.
AB - The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We propose two power-law kernels by generalizing Gaussian and Laplacian kernels. This generalization is based on distributions, arising out of maximization of a generalized information measure known as nonextensive entropy that is very well studied in statistical mechanics.We prove that the proposed kernels are positive definite, and provide some insights regarding the corresponding Reproducing Kernel Hilbert Space (RKHS). We also study practical significance of both kernels in classification and regression, and present some simulation results.
UR - http://www.scopus.com/inward/record.url?scp=84893344103&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84893344103
SN - 9781577356158
T3 - Proceedings of the 27th AAAI Conference on Artificial Intelligence, AAAI 2013
SP - 365
EP - 371
BT - Proceedings of the 27th AAAI Conference on Artificial Intelligence, AAAI 2013
T2 - 27th AAAI Conference on Artificial Intelligence, AAAI 2013
Y2 - 14 July 2013 through 18 July 2013
ER -