用神经网络建模变量依赖关系随协变量变化，理论有保障。
Covariate-dependent Graphical Model Estimation via Neural Networks with Statistical Guarantees
- 用神经网络建模图结构随协变量的动态变化
- 在非正态数据下仍能良好拟合，且理论保证成立
- 适合需要解释性的神经科学与金融数据分析
图形模型广泛用于刻画多个随机变量间的条件依赖关系。本文研究图结构随协变量变化的情形，提出基于深度神经网络的估计方法。该方法能灵活捕捉协变量对依赖关系的影响，在不假设数据服从正态分布的情况下仍具有良好拟合性能。在常用的经验风险最小化框架假设下，建立了具有概率保证（PAC）的理论结果。通过多个合成数据实验评估方法性能，并与现有方法对比。进一步在神经科学和金融领域的实际数据上验证，结果具有可解释性。
原文摘要 · Abstract (English)
Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and investigate a deep neural network-based approach to estimate it. The method allows for flexible functional dependency on the covariate, and fits the data reasonably well in the absence of a Gaussianity assumption. Theoretical results with PAC guarantees are established for the method, under assumptions commonly used in an Empirical Risk Minimization framework. The performance of the proposed method is evaluated on several synthetic data settings and benchmarked against existing approaches. The method is further illustrated on real datasets involving data from neuroscience and finance, respectively, and produces interpretable results.
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