Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due to their flexibility and efficiency. In this work, we consider Gaussian-gated localized MoE (GLoME) and block-diagonal covariance localized MoE (BLoME) regression models to present nonlinear relationships in heterogeneous data with potential hidden graph-structured interactions between high-dimensional predictors. These models pose difficult statistical estimation and model selection questions, both from a computational and theoretical perspective. This paper is devoted to the study of the problem of model selection among a collection of GLoME or BLoME models characterized by the number of mixture components, the complexity of Gaussian mean experts, and the hidden block-diagonal structures of the covariance matrices, in a penalized maximum likelihood estimation framework. In particular, we establish non-asymptotic risk bounds that take the form of weak oracle inequalities, provided that lower bounds for the penalties hold. The good empirical behavior of our models is then demonstrated on synthetic and real datasets.
This work is partially supported by the French Ministry of Higher Education and Research (MESRI), French National Research Agency (ANR) grant SMILES ANR-18-CE40-0014, Australian Research Council grant number DP180101192, and the Inria LANDER project.
TrungTin Nguyen is supported by a “Contrat doctoral” from the French Ministry of Higher Education and Research. Faicel Chamroukhi is granted by the French National Research Agency (ANR) grant SMILES ANR-18-CE40-0014. Hien Duy Nguyen is funded by Australian Research Council grant number DP180101192. This research is funded directly by the Inria LANDER project. TrungTin Nguyen also sincerely acknowledges Inria Grenoble-Rhône-Alpes Research Centre for a valuable Visiting PhD Fellowship working with STATIFY team so that this research can be completed, Erwan LE PENNEC and Lucie Montuelle for providing the simulations for the SGaME models. Finally, we thank the Editor-in-Chief, Associate Editor, and Reviewers for their valuable comments, which enabled us to produce a much improved manuscript.
"A non-asymptotic approach for model selection via penalization in high-dimensional mixture of experts models." Electron. J. Statist. 16 (2) 4742 - 4822, 2022. https://doi.org/10.1214/22-EJS2057