Dual-Homotopy Framework for Constrained EM Algorithm

TL;DR

This paper introduces a dual-homotopy framework for constrained EM algorithms, combining deterministic annealing and barrier methods to improve stability and accuracy in parameter estimation under constraints.

Contribution

It presents a novel dual-homotopy framework and an adaptive constrained EM algorithm that ensure stable, monotonic likelihood optimization under general constraints.

Findings

The proposed algorithm outperforms standard EM in stability and accuracy.

Simulation and real-data studies confirm improved estimation under constraints.

The method is applicable regardless of distributional form or constraint structure.

Abstract

We propose a new constrained EM algorithm that is applicable to general constrained estimation problems. The proposed method is based on a novel framework, the `dual-homotopy framework,' which combines deterministic annealing EM with a barrier-based optimization, enabling stable estimation under parameter constraints. Building on this framework, we further introduce an adaptive constrained EM algorithm that preserves likelihood monotonicity, regardless of the underlying distributional form or the specific structure of the constraints. Through simulation studies and a real-data analysis, both under parameter constraints, we demonstrate that the proposed algorithm yields more stable and accurate estimates than existing methods, including the standard EM algorithm.