Dot-product kernels is a large family of kernel functions based on dot-product between examples. A recent result states that any dot-product kernel can be decomposed as a non-negative linear combination of homogeneous polynomial kernels of different degrees, and it is possible to learn the coefficients of the combination by exploiting the Multiple Kernel Learning (MKL) paradigm. In this paper it is proved that, under mild conditions, any homogeneous polynomial kernel defined on binary valued data can be decomposed in a parametrized finite linear non-negative combination of monotone conjunctive kernels. MKL has been employed to learn the parameters of the combination. Furthermore, we show that our solution produces a deep kernel whose feature space consists of hierarchically organized features of increasing complexity. We also emphasize the connection between our solution and existing deep kernel learning frameworks. A wide empirical assessment is presented to evaluate the proposed framework, and to compare it against the baselines on several categorical and binary datasets.

Learning deep kernels in the space of monotone conjunctive polynomials

Lauriola I.;Polato M.;Aiolli F.
2020

Abstract

Dot-product kernels is a large family of kernel functions based on dot-product between examples. A recent result states that any dot-product kernel can be decomposed as a non-negative linear combination of homogeneous polynomial kernels of different degrees, and it is possible to learn the coefficients of the combination by exploiting the Multiple Kernel Learning (MKL) paradigm. In this paper it is proved that, under mild conditions, any homogeneous polynomial kernel defined on binary valued data can be decomposed in a parametrized finite linear non-negative combination of monotone conjunctive kernels. MKL has been employed to learn the parameters of the combination. Furthermore, we show that our solution produces a deep kernel whose feature space consists of hierarchically organized features of increasing complexity. We also emphasize the connection between our solution and existing deep kernel learning frameworks. A wide empirical assessment is presented to evaluate the proposed framework, and to compare it against the baselines on several categorical and binary datasets.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3382926
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact