Discussion of ‘ Correlated variables in regression : clustering and sparse estimation

نویسندگان

  • Peter Bühlmann
  • Philipp Rütimann
  • Sara van de Geer
  • Cun-Hui Zhang
  • Rajen D. Shah
  • Richard J. Samworth
چکیده

We would like to begin by congratulating the authors on their fine paper. Handling highly correlated variables is one of the most important issues facing practitioners in highdimensional regression problems, and in some ways it is surprising that it has not received more attention up to this point. The authors have made substantial progress towards practical methodological proposals, however, and we are sure the paper will stimulate considerable future research. In this discussion, we present a possible improvement to the cluster representative Lasso, give some further insights into the cluster group Lasso and conclude with some brief remarks on one possible new direction suggested by the work.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Robust Estimation in Linear Regression with Molticollinearity and Sparse Models

‎One of the factors affecting the statistical analysis of the data is the presence of outliers‎. ‎The methods which are not affected by the outliers are called robust methods‎. ‎Robust regression methods are robust estimation methods of regression model parameters in the presence of outliers‎. ‎Besides outliers‎, ‎the linear dependency of regressor variables‎, ‎which is called multicollinearity...

متن کامل

Sparse Estimation with Strongly Correlated Variables using Ordered Weighted `1 Regularization

This paper studies ordered weighted `1 (OWL) norm regularization for sparse estimation problems with strongly correlated variables. We prove sufficient conditions for clustering based on the correlation/colinearity of variables using the OWL norm, of which the so-called OSCAR [4] is a particular case. Our results extend previous ones for OSCAR in several ways: for the squared error loss, our co...

متن کامل

Efficient Clustering of Correlated Variables and Variable Selection in High-Dimensional Linear Models

In this paper, we introduce Adaptive Cluster Lasso(ACL) method for variable selection in high dimensional sparse regression models with strongly correlated variables. To handle correlated variables, the concept of clustering or grouping variables and then pursuing model fitting is widely accepted. When the dimension is very high, finding an appropriate group structure is as difficult as the ori...

متن کامل

Discussion of “correlated Variables in Regression: Clustering and Sparse Estimation”

Y = Xβ + ε. Here Y is the response vector in Rn, X is an n × p matrix, β0 ∈ Rp is the vector of coefficients, and finally ε ∈ Rn is assumed to be multivariate normal with mean zero and covariance matrix σ2I. While it has been shown that the lasso, and its many variants, “work” in terms of variable selection and prediction, they work best for near orthogonal cases of X. However, if p > n, correl...

متن کامل

Discussion of ‘Correlated variables in regression_ Clustering and sparse estimation’ by Peter Bühlmann, Philipp Rütimann, Sara van de Geer and Cun-Hui Zhang

We would like to begin by congratulating the authors on their fine paper. Handling highly correlated variables is one of the most important issues facing practitioners in high-dimensional regression problems, and in some ways it is surprising that it has not received more attention up to this point. The authors have made substantial progress towards practical methodological proposals, however, ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013