论文标题
针对一系列稀疏回归问题的投射神经网络（基数罚款）
Projection Neural Network for a Class of Sparse Regression Problems with Cardinality Penalty
论文作者
论文摘要
在本文中，我们考虑了一类稀疏回归问题，其目标函数是凸损失函数和基数惩罚的总结。通过为基数函数构建平滑函数，我们提出了一个投影的神经网络，并设计了一种解决此问题的校正方法。所提出的神经网络的解决方案是独特的，全球存在的，有界和全球Lipschitz的连续的。此外，我们证明所提出的神经网络的所有积累点都有一个共同的支持集，而非零条目的统一下限。将提出的神经网络与校正方法相结合，任何校正后的积累点都是被考虑的稀疏回归问题的局部最小化器。此外，我们分析了所考虑的稀疏回归问题与另一个回归稀疏问题之间的局部最小化关系的等效关系。最后，提供了一些数值实验，以显示拟议的神经网络在解决实践中一些稀疏回归问题方面的效率。
In this paper, we consider a class of sparse regression problems, whose objective function is the summation of a convex loss function and a cardinality penalty. By constructing a smoothing function for the cardinality function, we propose a projected neural network and design a correction method for solving this problem. The solution of the proposed neural network is unique, global existent, bounded and globally Lipschitz continuous. Besides, we prove that all accumulation points of the proposed neural network have a common support set and a unified lower bound for the nonzero entries. Combining the proposed neural network with the correction method, any corrected accumulation point is a local minimizer of the considered sparse regression problem. Moreover, we analyze the equivalent relationship on the local minimizers between the considered sparse regression problem and another regression sparse problem. Finally, some numerical experiments are provided to show the efficiency of the proposed neural networks in solving some sparse regression problems in practice.
