Tackling the subsampling problem to infer collective properties from limited data

Despite the development of large-scale data-acquisition techniques, experimental observations of complex systems are often limited to a tiny fraction of the system under study. This spatial subsampling is particularly severe in neuroscience, in which only a tiny fraction of millions or even billions of neurons can be individually recorded. Spatial subsampling may lead to substantial systematic biases when inferring the collective properties of the entire system naively from a subsampled part. To overcome such biases, powerful mathematical tools have been developed. In this Perspective, we give an overview of some issues arising from subsampling and review approaches developed in recent years to tackle the subsampling problem. These approaches enable one to correctly assess phenomena such as graph structures, collective dynamics of animals, neural network activity or the spread of disease from observing only a tiny fraction of the system. However, existing approaches are still far from having solved the subsampling problem in general, and we also outline what we believe are the main open challenges. Solving these challenges alongside the development of large-scale recording techniques will enable further fundamental insights into the workings of complex and living systems. For many complex or living systems, it is impossible to individually sample all their units, but subsampling can heavily bias the inference about their collective properties. This Perspective presents the subsampling problem and reviews recent developments to overcome this fundamental limitation.