Covariance Matrix Completion via Auxiliary Information

Oregon Convention Center 

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 covariation. 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 theoretically, via simulations, and in graphical model estimation from large-scale neuroscience data.

graphical models

missing data

regression

prediction

regularization

neuroscience 

IMS