The Double Dantzig
نویسندگان
چکیده
The Dantzig selector (Candes and Tao, 2007) is a new approach that has been proposed for performing variable selection and model fitting on linear regression models. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the Lasso. While both the Lasso and Dantzig selector potentially do a good job of selecting the correct variables, several researchers have noted that they tend to over shrink the final coefficients. This results in an unfortunate tradeoff. One can either select a high shrinkage tuning parameter that produces an accurate model but poor coefficient estimates or a low shrinkage tuning parameter that produces more accurate coefficients but includes many irrelevant variables. We propose a new approach called the “Double Dantzig”. The Double Dantzig has two key advantages over both the Dantzig selector and the Lasso. First, we demonstrate that it can select the correct model without over shrinking the coefficient estimates. Second, it can be applied to all standard generalized linear model response distributions. In addition we develop a path algorithm to simultaneously compute the coefficient estimates for all values of the tuning parameter, making our approach computationally efficient. A detailed simulation study is performed which illustrates the advantages of the Double Dantzig in relation to other possible methods. Finally, we demonstrate the Double Dantzig on several real world data sets. Some key words: Dantzig Selector; Double Dantzig; Generalized Linear Models; Lasso; Variable
منابع مشابه
Documentation for the R-code to implement the GDS methodology in “The Double Dantzig”
Description This is a set of functions that fit the Generalized Dantzig Selector (GDS) and the Double Dantzig (DD) approaches. The main fitting functions for GDS and DD are " gds() " and " dd() ". In addition " dd.cv() " performs cross-validation to choose the tuning parameter for the double dantzig procedure. We provide documentation for these functions below. Installation To install the softw...
متن کاملDantzig-wolfe Decomposition with Gams
This document illustrates the Dantzig-Wolfe decomposition algorithm using GAMS.
متن کاملGeorge B . Dantzig 1914 – 2005
Stanford News Service George B. Dantzig is well known as the father of linear programming. This “underestimates his paternal accomplishments” as is compellingly illustrated in the recent book [3] entitled The Basic George B. Dantzig. Dantzig made either fundamental or founding contributions in mathematical statistics, linear programming, network optimization, integer programming, nonlinear prog...
متن کاملDASSO: Connections Between the Dantzig Selector and Lasso
We propose a new algorithm, DASSO, for fitting the entire coefficient path of the Dantzig selector with a similar computational cost to the LARS algorithm that is used to compute the Lasso. DASSO efficiently constructs a piecewise linear path through a sequential simplex-like algorithm, which is remarkably similar to LARS. Comparison of the two algorithms sheds new light on the question of how ...
متن کامل