A1243
Title: Spacing test for generalized lasso with full row rank of D: Fused lasso and trend filtering
Authors: Rieko Tasaka - Osaka University Graduate School (Japan) [presenting]
Ryosuke Shimmura - Osaka University Graduate School (Japan)
Joe Suzuki - Osaka University (Japan)
Abstract: A generalized lasso is considered. In generalized lasso, fused lasso and trend filtering are exceptional cases in that the matrix $D$ in the objective function is full row rank. Fused lasso and trend filtering are methods for smoothing one-time and second-order differences. Given an $N$-dimensional observation vector $y$ and a constant > 0, an $N$-dimensional vector is obtained that minimizes the least-squares regression equation multiplied by a penalty term. A novel approach is proposed to solve the problem from the post-selective inference (PSI) perspective. In particular, a PSI method is considered called the spacing test, considered previously for linear regression Lasso. The spacing test assumes LARS, which is an approximation of lasso. Spaing tests the set of selected variables in which the null hypothesis is that all the necessary variables have been selected. The main contribution of the research is to modify the spacing test for choosing the appropriate value, which validates the choice of the fused lasso. The R program is made to execute the procedure to examine whether the proposed method works even for large N. The proposed method can also be considered similar to trend filtering, but unlike fused lasso, it cannot be solved by simply adding variables, as in LARS. Hence, it needs to be devised differently from a fused lasso.
