Inverse Ising Inference Using All the Data

    Phys. Rev. Lett. 108, 090201 – Published 1 March 2012
    Erik Aurell and Magnus Ekeberg

    Abstract

    We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for hundreds of nodes. The largest improvement in reconstruction occurs for strong interactions. Using two examples, a diluted Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of l1 regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.

    DOI: http://dx.doi.org/10.1103/PhysRevLett.108.090201

    • Figure
    • Figure
    • Received 29 September 2011
    • Revised 12 December 2011
    • Published 1 March 2012

    © 2012 American Physical Society

    Authors & Affiliations

    Erik Aurell*

    • ACCESS Linnaeus Centre, KTH, Stockholm, Sweden and Department Computational Biology, AlbaNova University Centre, 106 91 Stockholm, Sweden

    Magnus Ekeberg

    • Engineering Physics Program, KTH Royal Institute of Technology, 100 77 Stockholm, Sweden

    • *Also at Aalto University School of Science, Helsinki, Finland.eaurell@kth.se
    • ekeb@kth.se

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