Graphical Exponential Screening
This provides an incremental improvement for researchers and practitioners in statistics and machine learning working with high-dimensional graphical models.
The paper tackles the problem of estimating precision matrices in high-dimensional Gaussian graphical models by proposing graphical Exponential Screening (gES), an aggregation estimator that linearly combines individual estimators with different graphs to balance error and sparsity. Results show its risk is comparable to an oracle-selected best single-graph estimator, with numerical performance validated on simulated and real datasets against state-of-the-art methods.
In high dimensions we propose and analyze an aggregation estimator of the precision matrix for Gaussian graphical models. This estimator, called graphical Exponential Screening (gES), linearly combines a suitable set of individual estimators with different underlying graphs, and balances the estimation error and sparsity. We study the risk of this aggregation estimator and show that it is comparable to that of the best estimator based on a single graph, chosen by an oracle. Numerical performance of our method is investigated using both simulated and real datasets, in comparison with some state-of-art estimation procedures.