# Interactive Inference under Information Constraints

arXiv: https://arxiv.org/abs/2007.10976 · HTML: https://mlsanity.com/paper/2007.10976/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2020.

## Built on by (most cited first, 15 of 15)

- [Communication-constrained hypothesis testing: Optimality, robustness, and reverse data processing inequalities](https://mlsanity.com/paper/2206.02765/) (2022)
- [Simple Binary Hypothesis Testing under Local Differential Privacy and Communication Constraints](https://mlsanity.com/paper/2301.03566/) (2023)
- [The Role of Interactivity in Structured Estimation](https://mlsanity.com/paper/2203.06870/) (2022)
- [Nonparametric extensions of randomized response for private confidence sets](https://mlsanity.com/paper/2202.08728/) (2022)
- [Order-Optimal Sequential 1-Bit Mean Estimation in General Tail Regimes](https://mlsanity.com/paper/2604.07796/) (2026)
- [Robust Testing and Estimation under Manipulation Attacks](https://mlsanity.com/paper/2104.10740/) (2021)
- [Robust Estimation of Discrete Distributions under Local Differential Privacy](https://mlsanity.com/paper/2202.06825/) (2022)
- [Continual Mean Estimation Under User-Level Privacy](https://mlsanity.com/paper/2212.09980/) (2022)
- [Sequential 1-bit Mean Estimation with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2509.21940/) (2025)
- [Fundamental limits of over-the-air optimization: Are analog schemes optimal?](https://mlsanity.com/paper/2109.05222/) (2021)
- [Sequential Estimation under Multiple Resources: a Bandit Point of View](https://mlsanity.com/paper/2109.14703/) (2021)
- [Uniformity Testing in the Shuffle Model: Simpler, Better, Faster](https://mlsanity.com/paper/2108.08987/) (2021)
- [On Collaboration in Distributed Parameter Estimation with Resource Constraints](https://mlsanity.com/paper/2307.06442/) (2023)
- [Statistical Mean Estimation with Coded Relayed Observations](https://mlsanity.com/paper/2505.09098/) (2025)
- [A Distribution Testing Approach to Clustering Distributions](https://mlsanity.com/paper/2512.08376/) (2025)

## Abstract (arXiv)

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.