  Sparse networks can be found in a wide range of applications, such as
biological and communication networks. Inference of such networks from data has
been receiving considerable attention lately, mainly driven by the need to
understand and control internal working mechanisms. However, while most
available methods have been successful at predicting many correct links, they
also tend to infer many incorrect links. Precision is the ratio between the
number of correctly inferred links and all inferred links, and should ideally
be close to 100%. For example, 50% precision means that half of inferred links
are incorrect, and there is only a 50% chance of picking a correct one. In
contrast, this paper develops a method, based on variational Bayesian inference
and Gaussian processes, that focuses on inferring links with very high
precision. In addition, our method does not require full-state measurements and
effectively promotes both system stability and network sparsity. Monte Carlo
simulations illustrate that our method has 100% or nearly 100% precision, even
in the presence of noise. The method should be applicable to a wide range of
network inference contexts, including biological networks and power systems.
