Research map / Learning theory and algorithms / Sample complexity
Distributed estimation under communication limits
Derives rates for estimating distributions and means across machines with constrained communication.
49 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Sample complexity, keyword cluster “estimation · estimator · minimax”
State History Tried Checklist Preprints Who Export
Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
6 papers in 2023–24 and 13 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 1.8% to 4.0%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · Total Variation Classes Beyond 1d: Minimax Rates, and the Limitations of Linear Smoothers (NeurIPS 2016 · 47 citations)
- 2017 · Distributed Mean Estimation with Limited Communication (ICML 2017 · 145 citations)
- 2018 · The Nearest Neighbor Information Estimator is Adaptively Near Minimax Rate-Optimal (NeurIPS 2018 · 33 citations)
- 2019 · Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detection (NeurIPS 2019 · 55 citations)
- 2020 · List-Decodable Mean Estimation via Iterative Multi-Filtering (NeurIPS 2020 · 8 citations)
- 2021 · Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning) (NeurIPS 2021 · 9 citations)
- 2022 · List-Decodable Sparse Mean Estimation (NeurIPS 2022 · 0 citations)
- 2023 · Subset-Based Instance Optimality in Private Estimation (ICML 2023 · 1 citation)
- 2024 · Robust Nonparametric Regression under Poisoning Attack (AAAI 2024 · 8 citations)
- 2025 · Robust Distributed Estimation: Extending Gossip Algorithms to Ranking and Trimmed Means (NeurIPS 2025 · 1 citation)
- 2026 · Improved Distribution Estimation in $\ell_\infty$ (ICML 2026 · 0 citations)
Earliest papers here
- Total Variation Classes Beyond 1d: Minimax Rates, and the Limitations of Linear Smoothers (NeurIPS 2016 · 47 citations)
- Distributed Mean Estimation with Limited Communication (ICML 2017 · 145 citations)
- Communication-Efficient Distributed Learning of Discrete Distributions (NeurIPS 2017 · 21 citations)
What has been tried
38 papers here report 228 measured changes (a component added, removed or swapped, compared with a baseline): helped 64%, no clear effect 11%, hurt 17%, mixed 8%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| add Lipschitz-function projection correction to the initial estimate | Synthetic data, random attack · root ℓ2 error | No clear effect | Robust Nonparametric Regression under Poisoning Attack (AAAI 2024 · 8 citations) | |
| Use DB8 rather than Haar wavelets | Synthetic Doppler, known noise standard deviation · MSE | 0.068 ± 0.0035 -> 0.007 ± 0.0002 | Helped | Adaptive Estimation and Learning under Temporal Distribution Shift (ICML 2025 · 0 citations) |
| Refine the coordinate-wise median initialization with FastGD updates | MNIST, Fashion-MNIST, and CoverType · accuracy | Helped | Simple and Optimal Sublinear Algorithms for Mean Estimation (NeurIPS 2025 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 12 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- sample mean · 2 of 12 papers
- empirical mean · 2 of 12 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 19 papers; from OpenAlex and the papers' affiliations).
- University of California, Berkeley · 3 papers
- University of Wisconsin - Madison · 2 papers
- Apple · 2 papers
- Aarhus University · 2 papers
- Southeast University · 2 papers
- Tsinghua University · 2 papers
- University of California, San Diego · 2 papers
Use it
Download BibTeX of 35 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Minimax estimation rates (109 papers)
- Optimal mean estimation and subsampling (95 papers)
- Density and property estimation (86 papers)
- Statistical analysis of GAN estimators (22 papers)
Elsewhere in the topic
- Sample complexity of learning distributions (101 papers)
- Statistical-query lower bounds (85 papers)
- Computational thresholds in graphs and structure (84 papers)
- Learning halfspaces under noise (84 papers)
- Robust and surrogate-loss learning bounds (83 papers)
- Sample complexity of ranking and selection (80 papers)
- Learning under log-concave distributions (80 papers)
- PAC learnability theory (79 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).