In this paper, we propose an adaptive group Lasso deep neural network for high-dimensional function approximation where input data are generated from a dynamical system and the target function depends on few active variables or few linear combinations of variables. We approximate the target function by a deep neural network and enforce an adaptive group Lasso constraint to the weights of a suitable hidden layer in order to represent the constraint on the target function. Our empirical studies show that the proposed method outperforms recent state-of-the-art methods including the sparse dictionary matrix method, neural networks with or without group Lasso penalty.

翻译：在本文中,我们建议为高维功能近似设置一个适应性组群Lasso深神经网络,其中输入数据来自动态系统,目标功能取决于少数活跃变量或几分线性变量组合。我们比较深神经网络的目标功能,并强制实施适应性组群Lasso对适当隐藏层重量的限制,以表示对目标功能的限制。我们的实证研究表明,拟议方法优于最新最新的最新方法,包括稀有字典矩阵方法、有或无Lasso处罚组的神经网络。