|Title||Variable Selection for Support Vector Machines in Moderately High Dimensions.|
|Publication Type||Journal Article|
|Year of Publication||2016|
|Authors||Zhang, Xiang, Yichao Wu, Lan Wang, and Runze Li|
|Journal||J R Stat Soc Series B Stat Methodol|
|Date Published||2016 Jan|
The support vector machine (SVM) is a powerful binary classification tool with high accuracy and great flexibility. It has achieved great success, but its performance can be seriously impaired if many redundant covariates are included. Some efforts have been devoted to studying variable selection for SVMs, but asymptotic properties, such as variable selection consistency, are largely unknown when the number of predictors diverges to infinity. In this work, we establish a unified theory for a general class of nonconvex penalized SVMs. We first prove that in ultra-high dimensions, there exists one local minimizer to the objective function of nonconvex penalized SVMs possessing the desired oracle property. We further address the problem of nonunique local minimizers by showing that the local linear approximation algorithm is guaranteed to converge to the oracle estimator even in the ultra-high dimensional setting if an appropriate initial estimator is available. This condition on initial estimator is verified to be automatically valid as long as the dimensions are moderately high. Numerical examples provide supportive evidence.
|Alternate Journal||J R Stat Soc Series B Stat Methodol|
|Original Publication||Variable selection for support vector machines in moderately high dimensions.|
|PubMed Central ID||PMC4709852|
|Grant List||P50 DA010075 / DA / NIDA NIH HHS / United States |
P50 DA039838 / DA / NIDA NIH HHS / United States
R01 CA149569 / CA / NCI NIH HHS / United States
P01 CA142538 / CA / NCI NIH HHS / United States
P50 DA036107 / DA / NIDA NIH HHS / United States
Variable Selection for Support Vector Machines in Moderately High Dimensions.