Deep neural networks are famous for their high prediction accuracy, but they are also known for their black-box nature and poor interpretability. We consider the problem of variable selection, that is, selecting the input variables that have significant predictive power on the output, in deep neural networks. Most existing variable selection methods for neural networks are only applicable to shallow networks or are computationally infeasible on large datasets; moreover, they lack a control on the quality of selected variables. Here we propose a backward elimination procedure called SurvNet, which is based on a new measure of variable importance that applies to a wide variety of networks. More importantly, SurvNet is able to estimate and control the false discovery rate of selected variables empirically. Further, SurvNet adaptively determines how many variables to eliminate at each step in order to maximize the selection efficiency. The validity and efficiency of SurvNet are shown on various simulated and real datasets, and its performance is compared with other methods. Especially, a systematic comparison with knockoff-based methods shows that although they have more rigorous false discovery rate control on data with strong variable correlation, SurvNet usually has higher power.

深度神经网络以其高预测精度而闻名，但它们也因其黑盒性质和可解释性差而闻名。我们考虑变量选择问题，即在深度神经网络中选择对输出具有显着预测能力的输入变量。大多数现有的神经网络变量选择方法仅适用于浅层网络或在大型数据集上计算不可行；此外，他们缺乏对所选变量质量的控制。在这里，我们提出了一种称为 SurvNet 的反向消除程序，它基于一种适用于各种网络的变量重要性的新度量。更重要的是，SurvNet 能够根据经验估计和控制所选变量的错误发现率。更远，SurvNet 自适应地确定每一步要消除多少变量，以最大限度地提高选择效率。在各种模拟和真实数据集上展示了 SurvNet 的有效性和效率，并将其性能与其他方法进行了比较。特别是，与基于仿冒的方法的系统比较表明，尽管它们对具有强变量相关性的数据具有更严格的错误发现率控制，但 SurvNet 通常具有更高的功率。