The Role of Interactivity in Structured Estimation

  title={The Role of Interactivity in Structured Estimation},
  author={Jayadev Acharya and Cl{\'e}ment L. Canonne and Ziteng Sun and Himanshu Tyagi},
We study high-dimensional sparse estimation under three natural constraints: communication constraints, local privacy constraints, and linear measurements (compressive sensing). Without sparsity assumptions, it has been established that interactivity cannot improve the minimax rates of estimation under these information constraints. The question of whether interactivity helps with natural inference tasks has been a topic of active research. We settle this question in the affirmative for the… 


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