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Title: Graphical model inference with network-structured variables Authors:  David Rossell - Universitat Pompeu Fabra (Spain) [presenting]
Jack Jewson - Universitat Pompeu Fabra and Barcelona Graduate School of Economics (Spain)
Piotr Zwiernik - Universitat Pompeu Fabra (Spain)
Laura Battaglia - Barcelona School of Economics (Spain)
Stephen Hansen - Imperial College London (United Kingdom)
Abstract: A main practical challenge to using graphical models in applications is that the sample size is often limited relative to the number of parameters to be learned. We discuss applications where one has access to external network data that provides valuable external information and effectively increases the sample size. The motivation stems from depicting the relation between COVID19 and social network data, and between the stock market and economic indicators extracted from text data. We propose a graphical LASSO framework where likelihood penalties are guided by external data, and a spike-and-slab prior framework that depicts how partial correlations depend on external network data. We develop computational schemes and software implementations in R and probabilistic programming languages. Our applications show how one may significantly improve interpretation, statistical accuracy and out-of-sample prediction, in some instances using significantly sparser graphical models than would otherwise be necessary.