On Efficient and Scalable Computation of the Nonparametric Maximum Likelihood Estimator in Mixture Models

In this paper, we focus on the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our approach discretizes this infinite dimensional convex optimization problem by setting fixed support points for the NPMLE and optimizing over the mixing proportions. We propose an efficient and scalable semismooth Newton based augmented Lagrangian method (ALM). Our algorithm outperforms the state-of-the-art methods (Kim et al., 2020; Koenker and Gu, 2017), capable of handling $n \approx 10^6$ data points with $m \approx …

computation focus likelihood multivariate optimization paper scalable support