Different experimental technologies measure different aspects of a system and to differing depth and breadth. High-throughput assays have inherently high false-positive and false-negative rates. Moreover, each technology includes systematic biases of a different nature. These differences make network reconstruction from multiple data sets difficult and error-prone. Additionally, because of the rapid rate of progress in biotechnology, there is usually no curated exemplar data set from which one might estimate data integration parameters. To address these concerns, we have developed data integration methods that can handle multiple data sets differing in statistical power, type, size, and network coverage without requiring a curated training data set. Our methodology is general in purpose and may be applied to integrate data from any existing and future technologies. Here we outline our methods and then demonstrate their performance by applying them to simulated data sets. The results show that these methods select true-positive data elements much more accurately than classical approaches. In an accompanying companion paper, we demonstrate the applicability of our approach to biological data. We have integrated our methodology into a free open source software package named POINTILLIST.