Inference for High-dimensional Exponential Family Graphical Models

Probabilistic graphical models have been widely used to model complex systems and aid scientific discoveries. Most existing work on highdimensional estimation of exponential family graphical models, including Gaussian and Ising models, is focused on consistent model selection. However, these results do not characterize uncertainty in the estimated structure and are of limited value to scientists who worry whether their findings will be reproducible and if the estimated edges are present in the model due to random chance. In this paper, we propose a novel estimator for edge parameters in an exponential family graphical models. We prove that the estimator is √ n-consistent and asymptotically Normal. This result allows us to construct confidence intervals for edge parameters, as well as, hypothesis tests. We establish our results under conditions that are typically assumed in the literature for consistent estimation. However, we do not require that the estimator consistently recovers the graph structure. In particular, we prove that the asymptotic distribution of the estimator is robust to model selection mistakes and uniformly valid for a large number of data-generating processes. We illustrate validity of our estimator through extensive simulation studies.