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A useful application of hyperparameters
is the identification of sensible directions
within the space of and variables.
Consider the general case of an inverse covariance, decomposed into components
=
.
Treating the coefficient vector (with components )
as hyperparameter with hyperprior
results in a prior energy (error) functional
|
(463) |
The -dependent normalization
has to be included to obtain the correct
stationarity condition for .
The components
can be the components of a negative Laplacian,
for example,
=
or
=
.
In that case adapting the hyperparameters
means searching for sensible directions in the
space of or variables.
This technique has been called
Automatic Relevance Determination
by MacKay and Neal [170].
The positivity constraint for
can be implemented explicitly,
for example by using
=
or
=
.
Joerg_Lemm
2001-01-21