Interaction screening: Efficient and sample-optimal learning of ising models

Marc Vuffray, Sidhant Misra, Andrey Y. Lokhov, Michael Chertkov

    Research output: Contribution to journalConference articlepeer-review

    44 Citations (Scopus)

    Abstract

    We consider the problem of learning the underlying graph of an unknown Ising model on p spins from a collection of i.i.d. samples generated from the model. We suggest a new estimator that is computationally efficient and requires a number of samples that is near-optimal with respect to previously established information-theoretic lower-bound. Our statistical estimator has a physical interpretation in terms of "interaction screening". The estimator is consistent and is efficiently implemented using convex optimization. We prove that with appropriate regularization, the estimator recovers the underlying graph using a number of samples that is logarithmic in the system size p and exponential in the maximum coupling-intensity and maximum node-degree.

    Original languageEnglish
    Pages (from-to)2603-2611
    Number of pages9
    JournalAdvances in Neural Information Processing Systems
    Publication statusPublished - 2016
    Event30th Annual Conference on Neural Information Processing Systems, NIPS 2016 - Barcelona, Spain
    Duration: 5 Dec 201610 Dec 2016

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