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

Published online by Cambridge University Press:  22 March 2021

By
Jonathan Scarlett  and
Volkan Cevher
Edited by
Miguel R. D. Rodrigues  and
Yonina C. Eldar
Miguel R. D. Rodrigues
Affiliation:
University College London
Yonina C. Eldar
Affiliation:
Weizmann Institute of Science, Israel
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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.

Keywords

Fano’s inequalitygraphical model selectiongroup testingestimationoptimizationsampling
Type
Chapter
Information
Information-Theoretic Methods in Data Science , pp. 487 - 528
Publisher: Cambridge University Press
Print publication year: 2021

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