Title: On the rate of convergence of an over-parametrized deep neural network regression estimate learned by gradient descent Show Chinese title

Title: 关于通过梯度下降学习的过参数化深度神经网络回归估计的收敛速度

Abstract: Nonparametric regression with random design is considered. The $L_2$ error with integration with respect to the design measure is used as the error criterion. An over-parametrized deep neural network regression estimate with logistic activation function is defined, where all weights are learned by gradient descent. It is shown that the estimate achieves a nearly optimal rate of convergence in case that the regression function is $(p,C)$--smooth. Show Chinese abstract

Abstract: 考虑了具有随机设计的非参数回归问题。 以设计测度关于积分的 $L_2$ 误差作为误差准则。 定义了一个使用逻辑激活函数的过参数化深度神经网络回归估计量， 其中所有权重都通过梯度下降法学习。 结果表明，当回归函数是 $(p,C)$--光滑时，该估计量可以达到接近最优的收敛速度。