摘要
本文提出稳健Lq(0<q<∞)正则化模型,证明该模型解的全局渐近分布定理.应用该定理可进一步证明当0<q<1时所提出的模型具有变量选择一致性,从而具有良好的变量选择能力.基于所获得的理论结果,提出一类求解该模型的无参量加权迭代算法,并给出相应的正则化参数选择策略.数值试验表明本文提出的模型与算法可行、有效,有广泛的应用价值.
In this paper, we introduce the robust L q （0 〈q〈∞）regularization model, and then prove the global asymptotic distribution theorem for solutions of the model we propose. Applying the results, we can derive the model based on L q （0 q 1） regularization satisfying the consistent property of variable selection; in other words, it has the capacity of variable selection. To solve this model, we develop an iterative weighted algorithm without extra parameters, and give the corresponding strategy of selecting regularization parameters. The experiment results reveal that the algorithm we introduce is available, efficient and widely valuable.
出处
《中国科学：数学》
CSCD
北大核心
2010年第10期985-998,共14页
Scientia Sinica：Mathematica
基金
国家重点基础研究计划(批准号:2007CB311002)
国家自然科学基金(批准号:60975036
11001227)资助项目
