Robust estimation of graphical models with measurement error: False discovery control and sensitivity analysis

This paper addresses the problem of learning {Gaussian} graphical models from data contaminated by additive measurement error. Applying traditional procedures to the noisy data may result in many false discoveries. On the other hand, existing procedures that explicitly account for measurement error assume that the measurement error covariance is known or can be estimated precisely. We provide two practical alternatives for the common setting where this side information is not available. The first proposed method follows a partial identification approach and estimates a graph with controlled false discovery rate when given an upper bound on the measurement error variances. In many settings, the precise variance of the errors is unknown, but the scientist may still confidently specify an upper bound. The second framework is a sensitivity analysis that assesses the minimum amount of measurement error required to explain away an estimated edge. This yields an interpretable measure for practitioners to assess which estimated edges are robust and which may be simply due to measurement error. We derive theoretical guarantees and show good empirical performance in simulations. We further illustrate the practical utility of our procedures on a single-cell mRNA sequencing dataset.