Joint rank and variable selection for parsimonious estimation in a high-dimensional finite mixture regression model

TL;DR

This paper introduces a dimensionality reduction method for high-dimensional finite mixture regression models, combining predictor selection via Group-Lasso and rank reduction to improve estimation efficiency.

Contribution

It proposes a new estimator with fast convergence rates that simultaneously performs predictor selection and rank reduction in high-dimensional mixture models.

Findings

Estimator achieves fast convergence rates.

Effective predictor selection with Group-Lasso.

Dimensionality reduction enhances model interpretability.

Abstract

We study a dimensionality reduction technique for finite mixtures of high-dimensional multivariate response regression models. Both the dimension of the response and the number of predictors are allowed to exceed the sample size. We consider predictor selection and rank reduction to obtain lower-dimensional approximations. A class of estimators with a fast rate of convergence is introduced. We apply this result to a specific procedure, introduced in [11], where the relevant predictors are selected by the Group-Lasso.