Adaptive L1 Research Articles

Variable selection in the additive rate model for recurrent event data

In this paper, we investigate the variable selection problem for recurrent event data under the additive rate model. According to the explicit estimator of the regression coefficients of the additive rate model, a loss function is constructed. It has a form similar to the ordinary least squares of a linear regression model up to a constant. We develop variable selection procedures by penalizing the loss function with the adaptive L1 penalty and smoothly clipped absolute derivation penalty, respectively. Under some mild regularity conditions, the oracle properties of both procedures are established. Extensive simulation studies are conducted to examine the performance of our proposed procedures in finite samples. Finally, these methods are applied to the well-known chronic granulomatous disease study.

Parametric component detection and variable selection in varying-coefficient partially linear models

In this paper we are concerned with detecting the true structure of a varying-coefficient partially linear model. The first issue is to identify whether a coefficient is parametric. The second issue is to select significant covariates in both nonparametric and parametric portions. In order to simultaneously address both issues, we propose to combine local linear smoothing and the adaptive LASSO and penalize both the coefficient functions and their derivatives using an adaptive L1 penalty. We give conditions under which this new adaptive LASSO consistently identifies the significant variables and parametric components along with estimation sparsity. Simulated and real data analysis demonstrate the proposed methodology.

SU‐E‐T‐868: Beam Orientation Optimization for Intensity Modulated Radiation Therapy Using Adaptive L1 Minimization

Purpose: Beam orientation optimization (BOO) tries to find a solution which contains nonzero fluence map at only a small number of beam angles to achieve a dosimetric objective. This is equivalent to require that the solution fluence map is sparse at the beam angle level. As such, we develop a BOO algorithm via adaptive L1 minimization, an optimization scheme known to result in a sparse solution. Methods: In addition to the energy function for the dosimetric objective, we introduce a sparsity energy into the total energy function. The sparsity energy is obtained by first taking L2 norm of beamlet intensities within each angle and then taking weighted L1 norm over angles. Such an energy term favors solutions with nonvanishing fluence map at only a few beam angles. During optimization, the weighting factors in the L1 norm are adaptively adjusted. Starting with all candidate angles, the optimization process identifies unimportant orientations gradually and removes them without largely sacrificing the dosimetric objective. The whole process terminates when a target number of beams is achieved. Fluence map optimization (FMO) is then performed based on the optimized configuration and on unoptimized (equiangular) beams. The final FMO energy function values are compared to evaluate plan qualities. Results: In one typical prostate case, the plan quality is compared with that from unoptimized beam angles. We have further systematically validated our algorithm in the contexts of 5–9 coplanar beams for 5 prostate patients and 1 head‐and‐neck patient. It is found that our BOO algorithm can lead to lower FMO objective values in 28 out of 30 combinations of patients and target number of beams. Conclusions: The developed BOO algorithm utilizing adaptive L1 minimization is found to be effective for identifying important beam angles, which leads to better plan qualities than unoptimized beam configurations.