Interactive Inference under Information Constraints
This addresses foundational challenges in privacy-preserving and communication-efficient machine learning, with incremental advances in theoretical bounds.
The paper tackles the problem of distributed statistical inference under information constraints like communication limits and local differential privacy, focusing on goodness-of-fit testing and distribution estimation. It establishes optimal bounds for these tasks under interactive protocols, correcting prior gaps and showing an example where interactivity improves performance.
We study the role of interactivity in distributed statistical inference under information constraints, e.g., communication constraints and local differential privacy. We focus on the tasks of goodness-of-fit testing and estimation of discrete distributions. From prior work, these tasks are well understood under noninteractive protocols. Extending these approaches directly for interactive protocols is difficult due to correlations that can build due to interactivity; in fact, gaps can be found in prior claims of tight bounds of distribution estimation using interactive protocols. We propose a new approach to handle this correlation and establish a unified method to establish lower bounds for both tasks. As an application, we obtain optimal bounds for both estimation and testing under local differential privacy and communication constraints. We also provide an example of a natural testing problem where interactivity helps.