  Matrix completion based collaborative filtering is considered scalable and
effective for online service link prediction (e.g., movie recommendation) but
does not meet the challenges of link prediction in ecological networks. A
unique challenge of ecological networks is that the observed data are subject
to systematic imperfect detection, due to the difficulty of accurate field
sampling. In this work, we propose a new framework customized for ecological
bipartite network link prediction. Our approach starts with incorporating the
Poisson N-mixture model, a widely used framework in statistical ecology for
modeling imperfect detection of a single species in field sampling. Despite its
extensive use for single species analysis, this model has never been considered
for link prediction between different species, perhaps because of the complex
nature of both link prediction and N-mixture model inference. By judiciously
combining the Poisson N-mixture model with a probabilistic nonnegative matrix
factorization (NMF) model in latent space, we propose an intuitive statistical
model for the problem of interest. We also offer a scalable and
convergence-guaranteed optimization algorithm to handle the associated maximum
likelihood identification problem. Experimental results on synthetic data and
two real-world ecological networks data are employed to validate our proposed
approach.
