A Kernel Statistical Test of Independence (T69)
Arthur Gretton, Kenji Fukumizu, Choon-Hui Teo, Le Song, Bernhard Scholkopf, Alex Smola ¨

· Covariance operator: Cxy : G  F , f, Cxy g F = Ex,y [f (x)g (y)] - Ex [f (x)]Ey [g (y)]
1 0

Samp:128, Dim:1 % acceptance of H
0.8 0.6 0.4 0.2 0 0 0.5 1 PD HSICp HSICg

· Independence criterion: HSIC(Pxy ; F , G ) := Cxy 2 S H · Independence test: when Pxy = Px Py , mHSICemp 
D

l
=1

Angle (×/4)

l zl2 ,

zl  N (0, 1) i.i.d.

· Applications: independent subspace analysis verification, dependence of text and translation