Research map / Learning theory and algorithms / Sample complexity
Optimal mean estimation and subsampling
Develops optimal mean estimators and subsampling or resampling procedures with sharp guarantees.
95 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.
24 papers in 2023–24 and 18 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 7.2% to 5.5%.
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 · Global Analysis of Expectation Maximization for Mixtures of Two Gaussians (NeurIPS 2016 · 85 citations)
- 2017 · High-Dimensional Structured Quantile Regression (ICML 2017 · 6 citations)
- 2018 · $\ell_1$-regression with Heavy-tailed Distributions (NeurIPS 2018 · 2 citations)
- 2019 · The Kelly Growth Optimal Portfolio with Ensemble Learning (AAAI 2019 · 24 citations)
- 2020 · Maxmin Q-learning: Controlling the Estimation Bias of Q-learning (ICLR 2020 · 36 citations)
- 2021 · Nonuniform Negative Sampling and Log Odds Correction with Rare Events Data (NeurIPS 2021 · 8 citations)
- 2022 · $k$-Sliced Mutual Information: A Quantitative Study of Scalability with Dimension (NeurIPS 2022 · 5 citations)
- 2023 · Distributionally Robust Linear Quadratic Control (NeurIPS 2023 · 4 citations)
- 2024 · Sigmoid Gating is More Sample Efficient than Softmax Gating in Mixture of Experts (NeurIPS 2024 · 3 citations)
- 2025 · From Understanding Genetic Drift to a Smart-Restart Mechanism for Estimation-of-Distribution Algorithms (Journal Track) (AAAI 2025 · 0 citations)
- 2026 · Sobolev Regularized Score Difference Estimation in Diffusion Models (ICML 2026 · 0 citations)
Earliest papers here
- Global Analysis of Expectation Maximization for Mixtures of Two Gaussians (NeurIPS 2016 · 85 citations)
- Estimating Maximum Expected Value through Gaussian Approximation (ICML 2016 · 31 citations)
- Truthful Univariate Estimators (ICML 2016 · 22 citations)
What has been tried
78 papers here report 603 measured changes (a component added, removed or swapped, compared with a baseline): helped 61%, no clear effect 12%, hurt 20%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| use feature-label pairs and conditional distributions | CIFAR10 vs. CIFAR100, D_val · Pearson correlation | 0.763(0.02) -> 0.989(0.01) | Helped | Data Distribution Valuation (NeurIPS 2024 · 1 citation) |
| Downsample the major class during pairwise estimation | TikTok Screenshots test · ACC | 0.835 -> 0.824 | Hurt | Pairwise Maximum Likelihood For Multi-Class Logistic Regression Model With Multiple Rare Classes (ICML 2025) |
What reviewers will expect
Datasets and baselines named in the 15 papers of this approach from 2025–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- trimmed mean · 2 of 15 papers
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 42 papers; from OpenAlex and the papers' affiliations).
- University of Texas, Austin · 5 papers
- University of Texas at Austin · 4 papers
- Stanford University · 3 papers
- Carnegie Mellon University · 3 papers
- Microsoft · 3 papers
- Purdue University · 3 papers
- National University of Singapore · 2 papers
- Ecole Polytechnique · 2 papers
- Johns Hopkins University · 2 papers
- University of Chicago · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
Get alerts. Describe your idea in scime atlas and save it (free scime account): you get a weekly email when new preprints land close to it.
Related approaches
Same keyword cluster
- Minimax estimation rates (109 papers)
- Density and property estimation (86 papers)
- Distributed estimation under communication limits (49 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).