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

Effects of hidden nodes on network structure inference