  Objective: Modelling the associations from high-throughput experimental
molecular data has provided unprecedented insights into biological pathways and
signalling mechanisms. Graphical models and networks have especially proven to
be useful abstractions in this regard. Ad-hoc thresholds are often used in
conjunction with structure learning algorithms to determine significant
associations. The present study overcomes this limitation by proposing a
statistically-motivated approach for identifying significant associations in a
network.
  Methods and Materials: A new method that identifies significant associations
in graphical models by estimating the threshold minimising the $L_{\mathrm{1}}$
norm between the cumulative distribution function (CDF) of the observed edge
confidences and those of its asymptotic counterpart is proposed. The
effectiveness of the proposed method is demonstrated on popular synthetic data
sets as well as publicly available experimental molecular data corresponding to
gene and protein expression profiles.
  Results: The improved performance of the proposed approach is demonstrated
across the synthetic data sets using sensitivity, specificity and accuracy as
performance metrics. The results are also demonstrated across varying sample
sizes and three different structure learning algorithms with widely varying
assumptions. In all cases, the proposed approach has specificity and accuracy
close to 1, while sensitivity increases linearly in the logarithm of the sample
size. The estimated threshold systematically outperforms common ad-hoc ones in
terms of sensitivity while maintaining comparable levels of specificity and
accuracy. Networks from experimental data sets are reconstructed accurately
with respect to the results from the original papers.
