Working Paper: CEPR ID: DP17638
Authors: Jack Jewson; Li Li; Laura Battaglia; Stephen Hansen; David Rossell; Piotr Zwiernik
Abstract: A frequent challenge when using graphical models in applications is that the sample size is limited relative to the number of parameters to be learned. Our motivation stems from applications where one has external data, in the form of networks between variables, that provides valuable information to help improve inference. Specifically, we depict the relation between COVID cases and social and geographical network data, and between stock market returns and economic and policy networks extracted from text data. We propose a graphical LASSO framework where likelihood penalties are guided by the external network data. We also propose a spike-and-slab prior framework that depicts how partial correlations depend on the networks, which helps interpret the fitted graphical model and its relationship to the network. We develop computational schemes and software implementations in R and probabilistic programming languages. Our applications show how incorporating network data can significantly improve interpretation, statistical accuracy, and out-of-sample prediction, in some instances using significantly sparser graphical models than would have otherwise been estimated.
Keywords: Graphical Models; Bayesian Inference; Spike-and-Slab
JEL Codes: C11; C55
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| External network data (O36) | Graphical model accuracy (C52) |
| Social networks (Facebook connections) (Z13) | Positive partial correlations of COVID-19 infection rates (C29) |
| Geographical networks (R12) | Positive partial correlations of COVID-19 infection rates (C29) |
| Similar risk exposure (text data) (C55) | Similar stock return behaviors (G40) |
| Economic and policy networks (D85) | Precision matrix (stock return dependencies) (C10) |