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Abstract:
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Graphical models have been used extensively for modeling biological networks. However, unmeasured confounders and correlations among measurements are often overlooked during model fitting, which may lead to spurious scientific discoveries. In this paper, we consider the setting in which multiple measurements/replicates are taken for each independent subject. We propose to learn the structure of a latent variable graphical model with correlated replicates under the assumption that replicates for each independent subject follow a one-lag stationary vector autoregressive model. Furthermore, we assume that the effects induced by the unmeasured confounders are piecewise constant across the replicates. The proposed method results in a convex optimization problem with the lasso and the fused lasso penalty, which we solve using a block coordinate descent algorithm. Theoretical guarantees are established for parameter estimation. We demonstrate via extensive numerical studies that our method is able to estimate latent variable graphical models with correlated replicates more accurately than existing methods. Finally, we apply our proposal to a brain imaging dataset.
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