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  • 16 - An Introductory Guide to Fano’s Inequality with Applications in Statistical Estimation

  • 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 487-528

  • Summary

    Information theory plays an indispensable role in the development of algorithm-independent impossibility results, both for communication problems and for seemingly distinct areas such as statistics and machine learning. While numerous information-theoretic tools have been proposed for this purpose, the oldest one remains arguably the most versatile and widespread: Fano’s inequality. In this chapter, we provide a survey of Fano’s inequality and its variants in the context of statistical estimation, adopting a versatile framework that covers a wide range of specific problems. We present a variety of key tools and techniques used for establishing impossibility results via this approach, and provide representative examples covering group testing, graphical model selection, sparse linear regression, density estimation, and convex optimization.