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  • 4 - Information-Theoretic Bounds on Sketching

  • 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 104-133

  • Summary

    Approximate computation methods with provable performance guarantees are becoming important and relevant tools in practice. In this chapter we focus on sketching methods designed to reduce data dimensionality in computationally intensive tasks. Sketching can often provide better space, time, and communication complexity trade-offs by sacrificing minimal accuracy. This chapter discusses the role of information theory in sketching methods for solving large-scale statistical estimation and optimization problems. We investigate fundamental lower bounds on the performance of sketching. By exploring these lower bounds, we obtain interesting trade-offs in computation and accuracy. We employ Fano’s inequality and metric entropy to understand fundamental lower bounds on the accuracy of sketching, which is parallel to the information-theoretic techniques used in statistical minimax theory.