Research map / Learning theory and algorithms / Kernels and regression theory
High-dimensional linear regression theory
Analyze risk of least-squares, interpolators and SVR in high dimensions.
61 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Kernels and regression theory, keyword cluster “ridge · linear regression · regularization”
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.
20 papers in 2023–24 and 15 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 8.1% to 6.1%.
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 · A Nonlinear Regression Technique for Manifold Valued Data With Applications to Medical Image Analysis (CVPR 2016 · 44 citations)
- 2017 · Differentially Private Ordinary Least Squares (ICML 2017)
- 2018 · Hunting for Discriminatory Proxies in Linear Regression Models (NeurIPS 2018 · 15 citations)
- 2019 · On the number of variables to use in principal component regression (NeurIPS 2019 · 22 citations)
- 2020 · Dual Instrumental Variable Regression (NeurIPS 2020 · 16 citations)
- 2021 · Parameter-free HE-friendly Logistic Regression (NeurIPS 2021 · 9 citations)
- 2022 · A new similarity measure for covariate shift with applications to nonparametric regression (ICML 2022 · 6 citations)
- 2023 · Estimating Koopman operators with sketching to provably learn large scale dynamical systems (NeurIPS 2023 · 3 citations)
- 2024 · Flat Minima in Linear Estimation and an Extended Gauss Markov Theorem (ICLR 2024 · 0 citations)
- 2025 · Spurious Correlations in High Dimensional Regression: The Roles of Regularization, Simplicity Bias and Over-Parameterization (ICML 2025 · 0 citations)
- 2026 · Scaling Laws for Precision in High-Dimensional Linear Regression (ICML 2026 · 0 citations)
Earliest papers here
- A Nonlinear Regression Technique for Manifold Valued Data With Applications to Medical Image Analysis (CVPR 2016 · 44 citations)
- Joint quantile regression in vector-valued RKHSs (NeurIPS 2016 · 22 citations)
- Additive Approximations in High Dimensional Nonparametric Regression via the SALSA (ICML 2016 · 20 citations)
What has been tried
44 papers here report 283 measured changes (a component added, removed or swapped, compared with a baseline): helped 59%, no clear effect 12%, hurt 18%, mixed 11%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Choose k too small (k < d) in PCR | Simulation, in-distribution spiked covariance · risk | Hurt | No Double Descent in Principal Component Regression: A High-Dimensional Analysis (ICML 2024) |
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 35 papers; from OpenAlex and the papers' affiliations).
- Harvard University · 3 papers
- LPSM · 2 papers
- École Polytechnique · 2 papers
- Sorbonne Université · 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
- High-dimensional asymptotic generalization (82 papers)
- Double descent and overfitting (53 papers)
- Kernel ridge regression analysis (57 papers)
Elsewhere in the topic
- RKHS kernel methods (127 papers)
- Neural tangent kernel analysis (109 papers)
- Statistical perspectives on generalization (99 papers)
- Information-theoretic generalization bounds (94 papers)
- Kernel regression under shift (89 papers)
- Generalization theory of deep networks (67 papers)
- Empirical generalization measures (61 papers)
- PAC-Bayes bounds (39 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).