Comments on: 1-penalization for mixture regression models
نویسندگان
چکیده
We would like to wholeheartedly congratulate Professors Städler, Bühlmann and van de Geer for an interesting and important paper on developing the L1 regularization theory and methodology in finite mixture regression (FMR) models. An innovated reparametrization scheme is introduced to ensure equivariance under affine transformations and enhance the performance. Some nonasymptotic oracle inequalities on the average excess risk of the Lasso-type estimator are established in high dimensions, where the number of covariates can be much larger than the sample size. The authors also introduce an efficient EM-type algorithm combined with an improved coordinate descent for implementation. We appreciate the opportunity to comment on several aspects of this paper.
منابع مشابه
Comment to “ ` 1 - Penalization for Mixture Regression Models ” by Nicolas Städler , Peter Bühlmann , and Sara van de Geer Gábor
I would like to congratulate the authors for this very interesting contribution. The generalization of `1-penalized linear regression to the “mixture-of-Gaussian-regressions” model raises some very interesting questions both from theoretical and algorithmic points of view and the paper offers a variety of powerful tools to attack both problems. In this comment I would like to mention another di...
متن کاملUsing Regression based Control Limits and Probability Mixture Models for Monitoring Customer Behavior
In order to achieve the maximum flexibility in adaptation to ever changing customer’s expectations in customer relationship management, appropriate measures of customer behavior should be continually monitored. To this end, control charts adjusted for buyer’s/visitor’s prior intention to repurchase or visit again are suitable means taking into account the heterogeneity across customers. In the ...
متن کاملThe Family of Scale-Mixture of Skew-Normal Distributions and Its Application in Bayesian Nonlinear Regression Models
In previous studies on fitting non-linear regression models with the symmetric structure the normality is usually assumed in the analysis of data. This choice may be inappropriate when the distribution of residual terms is asymmetric. Recently, the family of scale-mixture of skew-normal distributions is the main concern of many researchers. This family includes several skewed and heavy-tailed d...
متن کاملHigh-Dimensional Sparse Econometric Models, an Introduction
In this chapter we discuss conceptually high dimensional sparse econometric models as well as estimation of these models using l1-penalization and postl1-penalization methods. Focusing on linear and nonparametric regression frameworks, we discuss various econometric examples, present basic theoretical results, and illustrate the concepts and methods with Monte Carlo simulations and an empirical...
متن کامل