Sparse Network Inference under Imperfect Detection and its Application to Ecological Networks

Abstract--Recovering latent structure from count data has received considerable attention in network inference, particularly when one seeks both cross-group interactions and within-group similarity patterns in bipartite networks, which is widely used in ecology research. Such networks are often sparse and inherently imperfect in their detection. Existing models mainly focus on interaction recovery, while the induced similarity graphs are much less studied. Moreover, sparsity is often not controlled, and scale is unbalanced, leading to oversparse or poorly rescaled estimates with degrading structural recovery. We impose nonconvex ℓ1/2 regularization on the latent similarity and connectivity structures to promote sparsity within-group similarity and cross-group connectivity with better relative scale. To solve it, we develop an ADMM-based algorithm with adaptive penalization and scale-aware initialization and establish its asymptotic feasibility and KKT stationarity of cluster points under mild regularity conditions. Experiments on synthetic and real-world ecological datasets demonstrate improved recovery of latent factors and similarity/connectivity structure relative to existing baselines. Index Terms--augmented Lagrangian, nonconvex nonsmooth optimization, nonnegative matrix factorization, link prediction, ecological network inference, structured sparse recovery I. INTRODUCTION This setting is inherent in sensing and monitoring applications [3], [4], where observations, such as counts, are obtained via an imperfect sampling process. In this paper, we are interested in ecological interaction networks describing how species associate with locations and how environments shape biodiversity patterns [5], [6].