How to automatically select the optimal hyperparameters?
|We have to optimize a
criterion which depends on the hyperparameters.
It is the Maximum
Likelihood Estimator on the observed image Y
w.r.t. and :
maximizing a probability w.r.t.
= set of images ,
with M grey levels
We use Bayes law to calculate the likelihood :
which exhibits the two following probability densities
||probability to obtain the data Y
from the initial image X,
(joint likelihood of X and hyperparameters)
probability on the image X
only taking into account the constraints
characterizes the type of regularization -function
André Jalobeanu - 24 Aug 1998