  Networks are a unifying framework for modeling complex systems and network
inference problems are frequently encountered in many fields. Here, I develop
and apply a generative approach to network inference (RCweb) for the case when
the network is sparse and the latent (not observed) variables affect the
observed ones. From all possible factor analysis (FA) decompositions explaining
the variance in the data, RCweb selects the FA decomposition that is consistent
with a sparse underlying network. The sparsity constraint is imposed by a novel
method that significantly outperforms (in terms of accuracy, robustness to
noise, complexity scaling, and computational efficiency) Bayesian methods and
MLE methods using l1 norm relaxation such as K-SVD and l1--based sparse
principle component analysis (PCA). Results from simulated models demonstrate
that RCweb recovers exactly the model structures for sparsity as low (as
non-sparse) as 50% and with ratio of unobserved to observed variables as high
as 2. RCweb is robust to noise, with gradual decrease in the parameter ranges
as the noise level increases.
