Research map / Learning theory and algorithms / Sample complexity
Minimax estimation rates
Derives optimal risk and rates for parametric and dependent-data estimators.
109 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Sample complexity, keyword cluster “estimation · estimator · minimax”
State History Tried 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.
23 papers in 2023–24 and 26 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 6.9% to 7.9%.
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 · Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues (ICML 2016 · 79 citations)
- 2017 · Approximate Supermodularity Bounds for Experimental Design (NeurIPS 2017 · 6 citations)
- 2018 · Learning Mixtures of Random Utility Models (AAAI 2018 · 35 citations)
- 2019 · Characterizing the Exact Behaviors of Temporal Difference Learning Algorithms Using Markov Jump Linear System Theory (NeurIPS 2019 · 34 citations)
- 2020 · Stable Learning via Sample Reweighting (AAAI 2020 · 122 citations)
- 2021 · Near-Optimal Linear Regression under Distribution Shift (ICML 2021 · 4 citations)
- 2022 · Convergence for score-based generative modeling with polynomial complexity (NeurIPS 2022 · 8 citations)
- 2023 · Classification of Heavy-tailed Features in High Dimensions: a Superstatistical Approach (NeurIPS 2023 · 4 citations)
- 2024 · Stopping Bayesian Optimization with Probabilistic Regret Bounds (NeurIPS 2024 · 5 citations)
- 2025 · Phase transitions for the existence of unregularized M-estimators in single index models (ICML 2025 · 1 citation)
- 2026 · Efficient and Minimax Optimal In-context Nonparametric Regression with Transformers (ICML 2026 · 0 citations)
Earliest papers here
- Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues (ICML 2016 · 79 citations)
- Interaction Screening: Efficient and Sample-Optimal Learning of Ising Models (NeurIPS 2016 · 46 citations)
- Multivariate tests of association based on univariate tests (NeurIPS 2016 · 18 citations)
What has been tried
85 papers here report 537 measured changes (a component added, removed or swapped, compared with a baseline): helped 67%, no clear effect 12%, hurt 16%, mixed 5%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Use the step-size schedule αₖ = c₀/√k instead of other tested powers | TD learning on Garnet problem · normal-approximation error Δₙ | n^{-1/4} | Helped | Gaussian Approximation and Multiplier Bootstrap for Polyak-Ruppert Averaged Linear Stochastic Approximation with Applications to TD Learning (NeurIPS 2024 · 2 citations) |
| Increase the LIPERM penalty coefficient λ from 0 on Swiss Roll | Swiss Roll · visual quality | No clear effect | Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution (ICML 2024 · 1 citation) | |
| use the D_n^* lattice instead of the integer or Barnes-Wall lattice | Speech · RDP tradeoff | Mixed | Optimal Neural Compressors for the Rate-Distortion-Perception Tradeoff (NeurIPS 2025 · 0 citations) | |
| Score methods using squared error in log-space instead of Itakura–Saito loss | All tested distributions and model sizes · Squared error in log-space | No clear effect | Estimating the Probabilities of Rare Outputs in Language Models (ICLR 2025 · 0 citations) | |
| Use compressed samples as both background and foreground instead of compressing only background data | 30 OpenML tasks · MAE | Mixed | Efficient and Accurate Explanation Estimation with Distribution Compression (ICLR 2025 · 0 citations) | |
| Use GP regression instead of CFL to estimate continuation risk | Two-class sequential Gaussian dataset · training time | 30 times faster | Helped | Learning the Optimal Stopping for Early Classification within Finite Horizons via Sequential Probability Ratio Test (ICLR 2025 · 0 citations) |
| Add truncation of likelihood ratios at threshold T | Moment estimation with bounded-tail likelihood ratios · stability | \lesssim \bar{b} \cdot r(n)^{\frac{\alpha}{\alpha+1}} | Helped | Minimax Optimal Two-Stage Algorithm For Moment Estimation Under Covariate Shift (ICLR 2025 · 0 citations) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 49 papers; from OpenAlex and the papers' affiliations).
- Renmin University of China · 4 papers
- EPFL · 3 papers
- Ben-Gurion University of the Negev · 2 papers
- University of Pennsylvania · 2 papers
- Massachusetts Institute of Technology · 2 papers
Use it
Download BibTeX of 40 key papersOpen the topic in the interactive map
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Related approaches
Same keyword cluster
- Optimal mean estimation and subsampling (95 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).