Marginalized Kernel

Kernel

K(x,y)=ϕ(x)Tϕ(y)ϕ(x)Fϕ(x):feature vectorF:feature space

Joint Kernel

KJ(x,y)=ϕ(vx,hx)Tϕ(vy,hy)x=(vx,hx),y=(vy,hy):variables with visible/hidden partsvx,vy:visible variableshx,hy:hidden variables

Marginalized Kernel

KM(x,y)=Ehx,hy[KJ(x,y)]=Ehx[ϕ(vx,hx)]TEhy[ϕ(vy,hy)]=ϕM(vx)TϕM(vy)ϕM(vx)=Ehx[ϕ(vx,hx)]:Marginalized Feature

Marginalized Count Kernel on HMM
Marginalized Count Kernel on SCFG

参考文献
[1] Koji Tsuda, Taishin Kin, Kiyoshi Asai, “Marginalized kernels for biological sequences”,
Bioinformatics, Volume 18, Issue suppl_1, 1 July 2002, Pages S268–S275
https://academic.oup.com/bioinformatics/article/18/suppl_1/S268/232208
[2] Taishin Kin, Koji Tsuda, Kiyoshi Asai,”Marginalized kernels for RNA sequence data analysis”,