Research map / Learning theory and algorithms / Sample complexity
Statistical-query lower bounds
Proves computational and sample lower bounds for learning halfspaces, distributions and high-dimensional statistics.
85 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Sample complexity, keyword cluster “al · bounds · et”
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.
16 papers in 2023–24 and 23 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic grew, from 4.8% to 7.0%.
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 · Parameter Learning for Log-supermodular Distributions (NeurIPS 2016 · 2 citations)
- 2017 · Linear regression without correspondence (NeurIPS 2017 · 50 citations)
- 2018 · Nearly Optimal Robust Subspace Tracking (ICML 2018 · 15 citations)
- 2019 · Near optimal finite time identification of arbitrary linear dynamical systems (ICML 2019 · 74 citations)
- 2020 · CLUB: A Contrastive Log-ratio Upper Bound of Mutual Information (ICML 2020 · 57 citations)
- 2021 · Tight High Probability Bounds for Linear Stochastic Approximation with Fixed Stepsize (NeurIPS 2021 · 8 citations)
- 2022 · The Franz-Parisi Criterion and Computational Trade-offs in High Dimensional Statistics (NeurIPS 2022 · 11 citations)
- 2023 · Unified Lower Bounds for Interactive High-dimensional Estimation under Information Constraints (NeurIPS 2023 · 8 citations)
- 2024 · Improved algorithm and bounds for successive projection (ICLR 2024 · 1 citation)
- 2025 · Pareto-frontier Entropy Search with Variational Lower Bound Maximization (ICML 2025 · 0 citations)
- 2026 · A Fine-Grained Understanding of Uniform Convergence for Halfspaces (ICML 2026 · 0 citations)
Earliest papers here
- Parameter Learning for Log-supermodular Distributions (NeurIPS 2016 · 2 citations)
- Linear regression without correspondence (NeurIPS 2017 · 50 citations)
- Practical Data-Dependent Metric Compression with Provable Guarantees (NeurIPS 2017 · 2 citations)
What has been tried
54 papers here report 359 measured changes (a component added, removed or swapped, compared with a baseline): helped 61%, no clear effect 11%, hurt 22%, 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 |
|---|---|---|---|---|
| add hyperplane projection | d >> log(n) · vertex-hunting error bound | factor of \sqrt{\log(n)/d} | Helped | Improved algorithm and bounds for successive projection (ICLR 2024 · 1 citation) |
| Use the MAP-based lower-bound estimator instead of the naive MC estimator | GP-generated synthetic functions, (d, L) = (2, 6) and (3, 6) · RHV | Helped | Pareto-frontier Entropy Search with Variational Lower Bound Maximization (ICML 2025 · 0 citations) | |
| Use batched updates instead of standard single-sample updates | Synthetic streaming PCA · sin²-error | Helped | Low Precision Streaming PCA (NeurIPS 2025 · 0 citations) | |
| Vary the H-matrix within the continuous family of optimal algorithms | Nonexpansive fixed-point problems · fixed-point residual norm squared | \frac{4 \norm{y_0-y_\star}^2}{N^2} | No clear effect | Optimal Acceleration for Minimax and Fixed-Point Problems is Not Unique (ICML 2024 · 0 citations) |
Recent preprints
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Who publishes on it
Institutions on the most papers of this approach since 2023 (of 39 papers; from OpenAlex and the papers' affiliations).
- Stanford University · 3 papers
- Purdue University · 3 papers
- Carnegie Mellon University · 2 papers
- University of Waterloo · 2 papers
- Indian Institute of Science · 2 papers
- University of California, San Diego · 2 papers
- Vector Institute · 2 papers
- University of Toronto · 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
- Robust and surrogate-loss learning bounds (83 papers)
- Computational thresholds in graphs and structure (84 papers)
- Generalization and limits under data constraints (72 papers)
Elsewhere in the topic
- Minimax estimation rates (109 papers)
- Sample complexity of learning distributions (101 papers)
- Optimal mean estimation and subsampling (95 papers)
- Density and property estimation (86 papers)
- Learning halfspaces under noise (84 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).