2025/05/22 by Michael Levine, Levine, Michael
Computer Science · Mathematics · #62G07 #62H30 #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Machine Learning and Algorithms #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2505.16878
openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this manuscript, we consider a finite nonparametric mixture model with non-independent marginal density functions. Dependence between the marginal densities is modeled using a copula device. Until recently, no deterministic algorithms capable of estimating components of such a model have been available. A deterministic algorithm that is capable of this has been proposed in \citet*levine2024smoothed. That algorithm seeks to maximize a smoothed nonparametric penalized log-likelihood; it seems to perform well in practice but does not possess the monotonicity property. In this manuscript, we introduce a deterministic MM (Minorization-Maximization) algorithm for estimation of components of this model that is also maximizing a smoothed penalized nonparametric log-likelihood but that is monotonic with respect to this objective functional. Besides the convergence of the objective functional, the convergence of a subsequence of arguments of this functional, generated by this algorithm, is also established. The behavior of this algorithm is illustrated using both simulated datasets as well as a real dataset. The results illustrate performance that is at least comparable to the earlier algorithm of \citet*levine2024smoothed. A discussion of the results and possible future research directions make up the last part of the manuscript.