Inverse finite-size scaling for high-dimensional significance analysis

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Details

Original languageEnglish
Article number062112
Pages (from-to)1-9
JournalPhysical Review E
Volume97
Issue number6
Publication statusPublished - 6 Jun 2018
MoE publication typeA1 Journal article-refereed

Researchers

Research units

  • University of Helsinki
  • University of Oslo
  • Tokyo Institute of Technology

Abstract

We propose an efficient procedure for significance determination in high-dimensional dependence learning based on surrogate data testing, termed inverse finite-size scaling (IFSS). The IFSS method is based on our discovery of a universal scaling property of random matrices which enables inference about signal behavior from much smaller scale surrogate data than the dimensionality of the original data. As a motivating example, we demonstrate the procedure for ultra-high-dimensional Potts models with order of 1010 parameters. IFSS reduces the computational effort of the data-testing procedure by several orders of magnitude, making it very efficient for practical purposes. This approach thus holds considerable potential for generalization to other types of complex models.

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