Discussion of: “Nonparametric regression using deep neural networks with ReLU activation function”
Discussion of: “Nonparametric regression using deep neural networks with ReLU activation function”
复制标题
DOI：
10.1214/19-aos1910
复制
发表时间：
2020-08
期刊：
影响因子：
--
通讯作者：
B. Ghorbani;Song Mei;Theodor Misiakiewicz;A. Montanari
中科院分区：
文献类型：
--
作者：
B. Ghorbani;Song Mei;Theodor Misiakiewicz;A. Montanari
对于g，GL1，.。。，GL1，...，LR：R→R(p，C)-光滑函数和x∈R的x1r单分量(对于两个不同的指数(L1，.。。，LR))。利用光滑样条族的惩罚最小二乘估计，证明了n−为2p/(2p+1)。Kohler和KrzyżAK(2017年)以所谓的广义层次交互模型的形式扩展了这一功能类，如下所述：
for g,gl1, . . . , gl1,...,lr : R → R (p,C)-smooth functions and x1r single components of x ∈ R (not necessarily different for two different indices (l1, . . . , lr )). With the use of a penalized least squares estimate for smoothing splines, they proved the rate n−2p/(2p+1). Kohler and Krzyżak (2017) extended this function class in form of the so-called generalized hierarchical interaction models introduced as follows: