Kernel Measures of Conditional Dependence
by K. Fukumizu, A. Gretton, X. Sun, and B. Schölkopf. ID: W3 Previous kernel measures depend on the choice of kernels. Defined by kernels, but kernel-free! Dependence Measure:


=

-1 / 2 ~~ YY

~~  Y X |Z 

-1 / 2 2 ~~ XX HS

defined using kernels
2

depends only on p.d.f.



 p XYZ ( x, y, z ) - p X |Z ( x | z ) pY |Z ( y | z ) pZ ( z )    p XZ ( x, z ) pYZ ( y, z )dxdydz   p XZ ( x, z ) pYZ ( y, z )  

holds for a wide class of kernels (e.g. Gaussian). ­ The proposed measures are used for independence and conditional independence tests.