Inferring relations from correlational data allows researchers across the sciences to uncover complex connections between variables for insights into the underlying mechanisms. The researchers often represent inferred relations using Gaussian graphical models, requiring regularization to sparsify the models. Acknowledging that the modular structure of the inferred network is often studied, we suggest module-based regularization to balance under- and overfitting. Compared with the graphical lasso, a standard approach using the Gaussian log-likelihood for estimating the regularization strength, this approach better recovers and infers modular structure in noisy synthetic and real data. The module-based regularization technique improves the usefulness of Gaussian graphical models in the many applications where they are employed.

翻译：从相关数据中推断关系使得各领域的科研人员能够揭示变量间的复杂联系，从而深入理解潜在机制。研究者常采用高斯图模型表示推断所得关系，并通过正则化方法实现模型稀疏化。鉴于推断网络的模块化结构常被作为研究对象，我们提出基于模块的正则化方法以平衡欠拟合与过拟合问题。相较于使用高斯对数似然估计正则化强度的标准方法——图套索算法，本方法在含噪声的合成数据与真实数据中能更有效地恢复和推断模块化结构。基于模块的正则化技术提升了高斯图模型在众多应用场景中的实用性。