A direct local search method and its application to a markovian model

TitleA direct local search method and its application to a markovian model
Publication TypeJournal Article
Year of Publication2017
AuthorsTaushanov, Z, Berchtold, A
JournalStatistics, optimization and information computing
Volume5
Pagination19-34
Date Publishedmar
Keywordsheuristic, Hidden Mixture Transition Distribution model, hill-climbing method, longitudinal data, optimization
Abstract

While the hidden mixture transition distribution (HMTD) model is a powerful framework for the description,analysis, and classification of longitudinal sequences of continuous data, it is notoriously difficult to estimate because of the complexity of its solution space. In this paper, we explore how a new heuristic specifically developed for the HMTD performs compared to different standard optimization algorithms. This specific heuristic can be classified as a hill-climbing method, and different variants are proposed, including a jittering procedure to escape local maxima and measures to speed up the convergence. Different popular approaches are used for comparison, including PSO, SA, GA, NM, L-BFGS-B, and DE. The same HMTD model was optimized on different datasets and the results were compared in terms of both fit to the data and estimated parameters. Even if the complexity of the problem implies that no one algorithm can be considered as an overall best, our heuristic performed well in all situations, leading to useful solutions in terms of both fit and interpretability. The principles presented in this paper can be easily applied to other similar statistical models with complex solution spaces.

DOI10.19139/soic.v5i1.253
Citation Key3104
Refereed DesignationRefereed