A fundamental problem associated with the task of network reconstruction from dynamical or behavioral data consists in determining the most appropriate model complexity in a manner that prevents overfitting, and produces an inferred network with a statistically justifiable number of edges. The status quo in this context is based on $L_{1}$ regularization combined with cross-validation. As we demonstrate, besides its high computational cost, this commonplace approach unnecessarily ties the promotion of sparsity with weight "shrinkage". This combination forces a trade-off between the bias introduced by shrinkage and the network sparsity, which often results in substantial overfitting even after cross-validation. In this work, we propose an alternative nonparametric regularization scheme based on hierarchical Bayesian inference and weight quantization, which does not rely on weight shrinkage to promote sparsity. Our approach follows the minimum description length (MDL) principle, and uncovers the weight distribution that allows for the most compression of the data, thus avoiding overfitting without requiring cross-validation. The latter property renders our approach substantially faster to employ, as it requires a single fit to the complete data. As a result, we have a principled and efficient inference scheme that can be used with a large variety of generative models, without requiring the number of edges to be known in advance. We also demonstrate that our scheme yields systematically increased accuracy in the reconstruction of both artificial and empirical networks. We highlight the use of our method with the reconstruction of interaction networks between microbial communities from large-scale abundance samples involving in the order of $10^{4}$ to $10^{5}$ species, and demonstrate how the inferred model can be used to predict the outcome of interventions in the system.

翻译：从动态或行为数据重构网络的核心问题在于，如何确定最合适的模型复杂度，以避免过拟合并生成具有统计合理边数的推断网络。当前主流方法基于$L_{1}$正则化结合交叉验证。然而，除计算成本高昂外，这种常规方法不必要地将稀疏性激励与权重“收缩”捆绑在一起。这种组合迫使我们在收缩引入的偏差与网络稀疏性之间权衡，即便经过交叉验证，也常导致严重过拟合。本文提出一种基于分层贝叶斯推断与权重量化的替代非参数正则化方案，该方案不依赖权重收缩来促进稀疏性。我们的方法遵循最小描述长度原则，揭示能使数据获得最大压缩的权重分布，从而无需交叉验证即可避免过拟合。后者使我们的方法只需对完整数据进行单次拟合，大幅提升运行效率。由此，我们获得一个可兼容多种生成模型的原则性高效推断方案，无需预先知道边的数量。实验表明，该方案在对人工网络与实证网络的重构中系统性提升精度。我们重点展示了该方法在大规模微生物群落互作网络重构中的应用（涉及$10^{4}$至$10^{5}$量级的物种丰度样本），并证明推断模型可用于预测系统干预结果。