# Over-the-Air Statistical Estimation

arXiv: https://arxiv.org/abs/2103.04014 · HTML: https://mlsanity.com/paper/2103.04014/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 6 Mar 2021.

## Builds on (most cited first, 25 of 25)

- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Convergence Time Optimization for Federated Learning over Wireless Networks](https://mlsanity.com/paper/2001.07845/) (2020)
- [Federated Learning for Edge Networks: Resource Optimization and Incentive Mechanism](https://mlsanity.com/paper/1911.05642/) (2019)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [Privacy For Free: Wireless Federated Learning Via Uncoded Transmission With Adaptive Power Control](https://mlsanity.com/paper/2006.05459/) (2020)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [Wireless Federated Learning with Local Differential Privacy](https://mlsanity.com/paper/2002.05151/) (2020)
- [Communication Lower Bounds for Statistical Estimation Problems via a Distributed Data Processing Inequality](https://mlsanity.com/paper/1506.07216/) (2015)
- [Wireless Federated Distillation for Distributed Edge Learning with Heterogeneous Data](https://mlsanity.com/paper/1907.02745/) (2019)
- [Geometric Lower Bounds for Distributed Parameter Estimation under Communication Constraints](https://mlsanity.com/paper/1802.08417/) (2018)
- [Inference under Information Constraints I: Lower Bounds from Chi-Square Contraction](https://mlsanity.com/paper/1812.11476/) (2018)
- [Convergence of Federated Learning over a Noisy Downlink](https://mlsanity.com/paper/2008.11141/) (2020)
- [Over-the-Air Computation Systems: Optimization, Analysis and Scaling Laws](https://mlsanity.com/paper/1909.00329/) (2019)
- [rTop-k: A Statistical Estimation Approach to Distributed SGD](https://mlsanity.com/paper/2005.10761/) (2020)
- [On Communication Cost of Distributed Statistical Estimation and Dimensionality](https://mlsanity.com/paper/1405.1665/) (2014)
- [Fisher information under local differential privacy](https://mlsanity.com/paper/2005.10783/) (2020)
- [Blind Over-the-Air Computation and Data Fusion via Provable Wirtinger Flow](https://mlsanity.com/paper/1811.04644/) (2018)
- [Over-the-Air Computation Systems: Optimal Design with Sum-Power Constraint](https://mlsanity.com/paper/2005.09139/) (2020)
- [Gradient Statistics Aware Power Control for Over-the-Air Federated Learning](https://mlsanity.com/paper/2003.02089/) (2020)
- [Lower Bounds for Learning Distributions under Communication Constraints via Fisher Information](https://mlsanity.com/paper/1902.02890/) (2019)
- [STAC: Simultaneous Transmitting and Air Computing in Wireless Data Center Networks](https://mlsanity.com/paper/1508.05935/) (2015)
- [Blind Federated Learning at the Wireless Edge with Low-Resolution ADC and DAC](https://mlsanity.com/paper/2010.00350/) (2020)

## Built on by (most cited first, 3 of 3)

- [Beyond Transmitting Bits: Context, Semantics, and Task-Oriented Communications](https://mlsanity.com/paper/2207.09353/) (2022)
- [PolarAir: A Compressed Sensing Scheme for Over-the-Air Federated Learning](https://mlsanity.com/paper/2301.10110/) (2023)
- [Over-the-Air Computation Aided Federated Learning with the Aggregation of Normalized Gradient](https://mlsanity.com/paper/2308.09082/) (2023)

## Abstract (arXiv)

We study schemes and lower bounds for distributed minimax statistical estimation over a Gaussian multiple-access channel (MAC) under squared error loss, in a framework combining statistical estimation and wireless communication. First, we develop "analog" joint estimation-communication schemes that exploit the superposition property of the Gaussian MAC and we characterize their risk in terms of the number of nodes and dimension of the parameter space. Then, we derive information-theoretic lower bounds on the minimax risk of any estimation scheme restricted to communicate the samples over a given number of uses of the channel and show that the risk achieved by our proposed schemes is within a logarithmic factor of these lower bounds. We compare both achievability and lower bound results to previous "digital" lower bounds, where nodes transmit errorless bits at the Shannon capacity of the MAC, showing that estimation schemes that leverage the physical layer offer a drastic reduction in estimation error over digital schemes relying on a physical-layer abstraction.