Covariate-dependent Graphical Model Estimation via Neural Networks with Statistical Guarantees
This work addresses the need for flexible graph structure estimation in fields like neuroscience and finance, though it appears incremental as it builds on existing neural network methods with added theoretical guarantees.
The paper tackles the problem of estimating covariate-dependent graphical models using a deep neural network approach, achieving flexible functional dependency and reasonable fit without Gaussian assumptions, with theoretical PAC guarantees and demonstrated performance on synthetic and real datasets.
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.