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Tackling the subsampling problem to infer collective properties from limited data

Nature Reviews Physics volume 4, pages 770–784 (2022)Cite this article

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Abstract

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.

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Fig. 1: Classes of subsampling.
Fig. 2: Sampling of dynamical observables.
Fig. 3: Scaling solutions for subsampled observations.
Fig. 4: Scaling theory can reveal macroscopic properties of collective dynamics despite windowed sampling.
Fig. 5: Subsampling-invariant measures.
Fig. 6: Reconstruction of a network under subsampling.

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Acknowledgements

The authors thank D. Dahmen, M. Helias, M. Henkel and P. Sollich for helpful discussions.

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Authors and Affiliations

  1. Eberhard Karls University of Tübingen, Tübingen, Germany

    Anna Levina

  2. Max Planck Institute for Biological Cybernetics, Tübingen, Germany

    Anna Levina

  3. Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany

    Viola Priesemann & Johannes Zierenberg

  4. Institute for the Dynamics of Complex Systems, University of Göttingen, Göttingen, Germany

    Viola Priesemann

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Levina, A., Priesemann, V. & Zierenberg, J. Tackling the subsampling problem to infer collective properties from limited data. Nat Rev Phys 4, 770–784 (2022). https://doi.org/10.1038/s42254-022-00532-5

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