论文标题
高维非凸套型$ m $估计器
High-dimensional nonconvex lasso-type $M$-estimators
论文作者
论文摘要
本文提出了一种$ \ ell_1 $ norm的理论，惩罚高维$ m $估计器，具有非凸风险和无限制的域。在高级条件下，估算器被证明可以达到收敛率$ s_0 \ sqrt {\ log（nd）/n} $，其中$ s_0 $是该息差的非零系数的数量。然后为我们的主要假设提供足够的条件，并最终在几个示例中使用，包括可靠的线性回归，二进制分类和非线性最小二乘。
This paper proposes a theory for $\ell_1$-norm penalized high-dimensional $M$-estimators, with nonconvex risk and unrestricted domain. Under high-level conditions, the estimators are shown to attain the rate of convergence $s_0\sqrt{\log(nd)/n}$, where $s_0$ is the number of nonzero coefficients of the parameter of interest. Sufficient conditions for our main assumptions are then developed and finally used in several examples including robust linear regression, binary classification and nonlinear least squares.
