论文标题
RKHS Ridge组的风险上限在回归模型中具有非高斯和非结合误差的风险上限
Risk upper bounds for RKHS ridge group sparse estimator in the regression model with non-Gaussian and non-bounded error
论文作者
论文摘要
我们考虑估计具有非高斯和非结合误差的未知回归模型的元模型的问题。元模型属于繁殖的内核希尔伯特空间，该空间是直接的希尔伯特空间总和，导致加性分解，包括变量及其之间的相互作用。该元模型的估计器是通过最大程度地减少受希尔伯特标准和经验$ l^2 $ norm的总和来惩罚的经验最小二乘标准来计算得出的。在这种情况下，建立了经验$ l^2 $风险的上限和$ l^2 $的估计风险。
We consider the problem of estimating a meta-model of an unknown regression model with non-Gaussian and non-bounded error. The meta-model belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to an additive decomposition including the variables and interactions between them. The estimator of this meta-model is calculated by minimizing an empirical least-squares criterion penalized by the sum of the Hilbert norm and the empirical $L^2$-norm. In this context, the upper bounds of the empirical $L^2$ risk and the $L^2$ risk of the estimator are established.
