O'Reilly logo

Pattern Recognition by Matthias Nagel, Matthias Richter, Jürgen Beyerer

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

p( b|a )=p( b ).( 2.205 )

Definition 2.12 (Induced uncorrelatedness). If two random variables are independent, then they are also uncorrelated. The converse is not necessarily true.

As an example, let a ∼ N(0,1) and b:= a2. Certainly, a and b are not stochastically independent, since if b is observed, one knows the magnitude |a| of a. If a is observed, one knows b. Nevertheless, a and b are uncorrelated, because Cov {a, b ∝ E {a3} = 0 since the third central moment of a Gaussian distribution is zero.

As already mentioned, the ICA is composed of two steps (see Figure 2.39). Instead of directly looking for a matrix U such that

m _ =U( m _ E{ m _ } )

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required