Natural order recovery for banded covariance models

Banded covariance models have recently received attention in the high dimensional covariance estimation literature. Banded inverse covariance models correspond to autoregressive processes and thus have a simple and intuitive interpretation, offering insight into underlying covariance structure. While a body of asymptotic results for banded estimators exists in the literature, these methods assume knowledge of a natural variable ordering. Although such an ordering may be known a priori, for example with time series data, in other settings it must be inferred before banding approaches can be applied. In this paper, we present a new method for recovering order of random variables based on Gaussian graphical modelling when the underlying inverse covariance matrices are banded or differentially banded. We demonstrate our algorithm on both synthetic and real data, and compare our results with the only other published order recovery method.