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Estimation of graph parameters based on a collection of graphs is essentialfor a wide range of graph inference tasks. In practice, weighted graphs aregenerally observed with edge contamination. We consider a weighted latentposition graph model contaminated via an edge weight gross error model andpropose an estimation methodology based on robust Lq estimation followed bylow-rank adjacency spectral decomposition. We demonstrate that, underappropriate conditions, our estimator both maintains Lq robustness and wins thebias-variance tradeoff by exploiting low-rank graph structure. We illustratethe improvement offered by our estimator via both simulations and a humanconnectome data experiment.

Robust Estimation from Multiple Graphs under Gross Error Contamination