A1239
Title: Computing the compatibility constant for the lasso by numerical optimization
Authors: Kei Hirose - Kyushu University (Japan) [presenting]
Abstract: The compatibility constant plays an important role in evaluating the prediction error of the lasso in high-dimensional settings. However, the computation of the compatibility constant is generally difficult because it is a complicated nonconvex optimization problem. A numerical approach is presented to compute the compatibility constant when the support of true regression coefficients is given. The optimization problem reduces to a quadratic programming (QP) once the signs of the nonzero coefficients are specified. In this case, the compatibility constant can be obtained by solving QPs for all possible sign combinations. A mixed-integer QP (MIQP) approach is also formulated that can be applied when the number of true nonzero coefficients is large. The finite-sample behavior of the compatibility constant for simulated data is investigated under various parameter settings and compared with its theoretical upper bound. The behavior of the compatibility constant in finite samples is also examined through real data analysis.
