  This paper addresses maximum likelihood (ML) estimation based model fitting
in the context of extrasolar planet detection. This problem is featured by the
following properties: 1) the candidate models under consideration are highly
nonlinear; 2) the likelihood surface has a huge number of peaks; 3) the
parameter space ranges in size from a few to dozens of dimensions. These
properties make the ML search a very challenging problem, as it lacks any
analytical or gradient based searching solution to explore the parameter space.
A population based searching method, called estimation of distribution
algorithm (EDA), is adopted to explore the model parameter space starting from
a batch of random locations. EDA is featured by its ability to reveal and
utilize problem structures. This property is desirable for characterizing the
detections. However, it is well recognized that EDAs can not scale well to
large scale problems, as it consists of iterative random sampling and model
fitting procedures, which results in the well-known dilemma curse of
dimensionality. A novel mechanism to perform EDAs in interactive random
subspaces spanned by correlated variables is proposed and the hope is to
alleviate the curse of dimensionality for EDAs by performing the operations of
sampling and model fitting in lower dimensional subspaces. The effectiveness of
the proposed algorithm is verified via both benchmark numerical studies and
real data analysis.
