Covariate-dependent Graphical Model Estimation via Neural Networks with Statistical Guarantees
Abstract: 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.
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: * Section 1: added related work for estimating graphical models based on a score matrix-based formulation; added Table 1 that summarizes extant literature on covariate-dependent graphical model
* Section 2: further elaborated on the exact functional form adopted; added Remark 3 (Section 2) that discusses how to obtain a sparsified graph via thresholding
* Section 3: added theoretical result for edge-level recovery (Corollary 2)
* Section 6: added a brief discussion that compares and contrasts the formulation adopted in this paper vs a potential alternative based on the score matrix
* Appendix E: Added a sentence outlining how hyper parameters are selected.
Code: https://github.com/GeorgeMichailidis/covariate-dependent-graphical-model
Assigned Action Editor: ~Jean_Honorio1
Submission Number: 3858
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