# Maximum Likelihood Estimation based on Random Subspace EDA: Application to Extrasolar Planet Detection

## TL;DR

This paper introduces a novel subspace-based estimation of distribution algorithm to improve maximum likelihood estimation for complex, high-dimensional models in extrasolar planet detection, addressing the curse of dimensionality.

## Contribution

It proposes a new interactive random subspace mechanism for EDAs, enhancing scalability in high-dimensional, nonlinear likelihood surface exploration.

## Key findings

- Effective in numerical benchmarks
- Successful application to real data
- Reduces dimensionality challenges in ML estimation

## Abstract

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.