  Effects of hidden nodes on inference quality of observed network structure
are explored based on a disordered Ising model with hidden nodes. We first
study analytically small systems consisting of a few nodes, and find that the
magnitude of the effective coupling grows as the coupling strength from the
hidden common input nodes increases, while the field strength of the input node
has opposite effects. Insights gained from analytic results of small systems
are confirmed in numerical simulations of large systems. We also find that the
inference quality deteriorates as the number of hidden nodes increases.
Furthermore, increasing field variance of hidden nodes improves the inference
quality of the effective couplings, but worsens the quality for the effective
fields. In addition, attenuated coupling strengths involved in at least one
hidden node lead to high quality of coupling inference.
