  Covariance matrix estimation is an important task in the analysis of
multivariate data in disparate scientific fields, including neuroscience,
genomics, and astronomy. However, modern scientific data are often incomplete
due to factors beyond the control of researchers, and data missingness may
prohibit the use of traditional covariance estimation methods. Some existing
methods address this problem by completing the data matrix, or by filling the
missing entries of an incomplete sample covariance matrix by assuming a
low-rank structure. We propose a novel approach that exploits auxiliary
variables to complete covariance matrix estimates. An example of auxiliary
variable is the distance between neurons, which is usually inversely related to
the strength of neuronal correlation. Our method extracts auxiliary information
via regression, and involves a single tuning parameter that can be selected
empirically. We compare our method with other matrix completion approaches via
simulations, and apply it to the analysis of large-scale neuroscience data.
