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.
Highlights
Many studies deal with the problem of finding the optimum of a function without using its derivatives
We present a search method with hill-climbing features designed to deal with the maximization of the log-likelihood of a hidden mixture transition distribution (HMTD) model for continuous variables, but which could be used in many other problems that have similar characteristics
We describe the different numerical experiments performed to evaluate the performance of our heuristic when used with the HMTD model
Summary
Many studies deal with the problem of finding the optimum of a function without using its derivatives. We present a search method with hill-climbing features designed to deal with the maximization of the log-likelihood of a hidden mixture transition distribution (HMTD) model for continuous variables, but which could be used in many other problems that have similar characteristics. One advantage of this method appears when we do not have a fixed set of constraints, but we cannot accept all mathematically correct solutions. We briefly present the HMTD model, followed by our heuristic estimation procedure, which we compare with some other well-known heuristic methods, and we present and analyse the results of different numerical experiments
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