The curse of dimensionality is a challenging issue in network science: the problem of inferring the network structure from sparse and noisy data becomes more and more difficult, indeed, as their dimensionality increases. We here develop a general strategy for dimensional reduction using iteratively thresholded ridge regression screener, one statistical method aiming to resolve the problem of variable selection. After drastically reducing the dimensions of the problem, we then employ the lasso method, a convex optimization method, to recover the network structure. We demonstrate the efficiency of the dimensional reduction method, and particular suitability for the natural sparsity of complex networks, in which the average degree is much smaller than their total number of nodes. Analysis based on various game dynamics and network topologies show that higher reconstruction accuracies and smaller reconstruction times can be achieved by our method. Our approach provides, therefore, a novel insight to solve the reconstruction problem and has potential applications in a wide range of fields.

中文翻译：

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通过安全降维恢复基于演化博弈动力学的网络结构

维数诅咒是网络科学中的一个具有挑战性的问题：实际上，随着维数的增加，从稀疏和嘈杂的数据中推断网络结构的问题变得越来越困难。我们在这里开发了一种使用迭代阈值岭回归筛选器进行降维的通用策略，这是一种旨在解决变量选择问题的统计方法。在大幅降低问题的维度后，我们使用 lasso 方法（一种凸优化方法）来恢复网络结构。我们证明了降维方法的效率，特别适用于复杂网络的自然稀疏性，其中平均度数远小于节点总数。基于各种博弈动力学和网络拓扑结构的分析表明，我们的方法可以实现更高的重建精度和更短的重建时间。因此，我们的方法为解决重建问题提供了一种新颖的见解，并在广泛的领域具有潜在的应用。