Network structure from rich but noisy data

Driven by growing interest across the sciences, a large number of empirical studies have been conducted in recent years of the structure of networks ranging from the Internet and the World Wide Web to biological networks and social networks. The data produced by these experiments are often rich and multimodal, yet at the same time they may contain substantial measurement error 1 – 7 . Accurate analysis and understanding of networked systems requires a way of estimating the true structure of networks from such rich but noisy data 8 – 15 . Here we describe a technique that allows us to make optimal estimates of network structure from complex data in arbitrary formats, including cases where there may be measurements of many different types, repeated observations, contradictory observations, annotations or metadata, or missing data. We give example applications to two different social networks, one derived from face-to-face interactions and one from self-reported friendships. A technique allows optimal inference of the structure of a network when the available observed data are rich but noisy, incomplete or otherwise unreliable.