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  • 13 - Statistical Problems with Planted Structures: Information-Theoretical and Computational Limits

  • Edited by Miguel R. D. Rodrigues, University College London, Yonina C. Eldar, Weizmann Institute of Science, Israel
  • Book:
    Information-Theoretic Methods in Data Science
    Published online:
    22 March 2021
    Print publication:
    08 April 2021, pp 383-424

  • Summary

    This chapter provides a survey of the common techniques for determining the sharp statistical and computational limits in high-dimensional statistical problems with planted structures, using community detection and submatrix detection problems as illustrative examples. We discuss tools including the first- and second-moment methods for analyzing the maximum-likelihood estimator, information-theoretic methods for proving impossibility results using mutual information and rate-distortion theory, and methods originating from statistical physics such as the interpolation method. To investigate computational limits, we describe a common recipe to construct a randomized polynomial-time reduction scheme that approximately maps instances of the planted clique problem to the problem of interest in total variation distance.