# Application of Information Theory to Blind Source Separation

Introduction :: BSS :: Mackay's Approach :: Natural Gradient :: p(u)

##
So what about
*
p
*
(
*
u
*
)

We have observed that if , then the last terms of the density go away. We also commented above that the given form works only for super-Gaussian sources. So what do we do in the case where this is not a good assumption. One approach is to deal with two densities. On the one hand, we take

giving (where

This

*p*is subGaussian. When and = 1 we obtain

and the learning rule (employing natural gradient) is

The superGaussian density is modeled as

giving rise to

and the learning rule

Combining these, we obtain

The decision between rules can be made on an element-by-element basis. A decision must be based on the available data.