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A product ansatz has the form
|
(403) |
where
=
represents projections
of the vector consisting of all and components.
The ansatz can be made more flexible by using sum of products
|
(404) |
The restriction of the trial space to product functions
corresponds to the Hartree approximation in physics.
(In a Hartree-Fock approximation
the product functions are antisymmetrized under coordinate exchange.)
For additive
=
with acting only on , i.e.,
=
,
with the projector into the space of functions
=
,
the quadratic regularization term becomes,
assuming
=
,
|
(405) |
For =
with a product structure with respect to
|
(406) |
In both cases the prior term factorizes into lower dimensional
contributions.
Next: Decision trees
Up: Parameterizing likelihoods: Variational methods
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Joerg_Lemm
2001-01-21