Research map / Learning theory and algorithms / Matrix and tensor methods
High-dimensional estimation theory
Analyzes spectral and message-passing estimators in high-dimensional regression and multi-index models.
89 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Matrix and tensor methods, keyword cluster “sparse · recovery · pca”
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.
14 papers in 2023–24 and 13 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 8.1% 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 · Estimating Structured Vector Autoregressive Models (ICML 2016 · 39 citations)
- 2017 · Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition (NeurIPS 2017 · 78 citations)
- 2018 · Leveraged volume sampling for linear regression (NeurIPS 2018 · 43 citations)
- 2019 · ALISTA: Analytic Weights Are As Good As Learned Weights in LISTA (ICLR 2019 · 98 citations)
- 2020 · Quasi-Newton Solver for Robust Non-Rigid Registration (CVPR 2020 · 53 citations)
- 2021 · On Path Integration of Grid Cells: Group Representation and Isotropic Scaling (NeurIPS 2021 · 3 citations)
- 2022 · Estimation in Rotationally Invariant Generalized Linear Models via Approximate Message Passing (ICML 2022 · 11 citations)
- 2023 · Clifford Group Equivariant Neural Networks (NeurIPS 2023 · 8 citations)
- 2024 · Exploiting Data Geometry in Machine Learning (AAAI 2024 · 1 citation)
- 2025 · Neural Networks Perform Sufficient Dimension Reduction (AAAI 2025 · 3 citations)
- 2026 · Learning Gaussian Graphical Models from a Glauber Trajectory Without Mixing (ICML 2026 · 0 citations)
Earliest papers here
- Estimating Structured Vector Autoregressive Models (ICML 2016 · 39 citations)
- Mixed Linear Regression with Multiple Components (NeurIPS 2016 · 29 citations)
- Trace Quotient Meets Sparsity: A Method for Learning Low Dimensional Image Representations (CVPR 2016 · 19 citations)
What has been tried
80 papers here report 602 measured changes (a component added, removed or swapped, compared with a baseline): helped 65%, no clear effect 10%, hurt 20%, mixed 4%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Add rank regularization to a vanilla neural network | Seoul weather test data · testing error (mean) | 0.774 -> 0.602 | Helped | Neural Networks Perform Sufficient Dimension Reduction (AAAI 2025 · 3 citations) |
| add filter transform | 2D Harmonic λ1 · absolute error | 6.73e-5 -> 1.02e-5 | Helped | STNet: Spectral Transformation Network for Solving Operator Eigenvalue Problem (NeurIPS 2025 · 1 citation) |
| Use proximal matching instead of squared ℓ2 loss | 1-D Laplacian denoising · match to ground-truth proximal | Helped | What's in a Prior? Learned Proximal Networks for Inverse Problems (ICLR 2024 · 1 citation) | |
| use estimated rank 3 or 4 instead of ground-truth rank 5 | Synthetic data, 3 and 10 subspaces · recovery error | 0.1330 -> 0.8827; 0.1372 -> 0.9164 | Hurt | Multi-Subspace Matrix Recovery from Permuted Data (AAAI 2025 · 0 citations) |
| Use 10 instead of 5 unrolls | Coronal PD, R=4 · PSNR | 40.94 -> 40.99 | No clear effect | Time-Embedded Algorithm Unrolling for Computational MRI (NeurIPS 2025 · 0 citations) |
| Increase embedding dimension K while using raw M | Analogy tasks · analogy completion accuracy | Mixed | On the Emergence of Linear Analogies in Word Embeddings (NeurIPS 2025 · 0 citations) | |
| Increase LongSync cycle length from 4 to 5 | Uniform corruption model · mean rotation estimation error | Helped | Efficient Detection of Long Consistent Cycles and its Application to Distributed Synchronization (CVPR 2024 · 0 citations) | |
| Add the time-aggregated network | CitiBike hourly networks (month-aggregated network) · cosine similarity | 214% | Helped | Inferring Dynamic Networks from Marginals with Iterative Proportional Fitting (ICML 2024 · 0 citations) |
| Train γ rather than fix it during preconditioning | Gaussian random walk design matrix · support recovery rate | Helped | Be a Goldfish: Forgetting Bad Conditioning in Sparse Linear Regression via Variational Autoencoders (ICML 2025) |
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 27 papers; from OpenAlex and the papers' affiliations).
- Swiss Federal Institute of Technology Lausanne · 4 papers
- EPFL · 3 papers
- Johns Hopkins University · 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
- Sparse regression with guarantees (94 papers)
- Signal recovery and phase retrieval (66 papers)
- Sparse and robust PCA (66 papers)
- Nonconvex low-rank and sparse optimization (112 papers)
Elsewhere in the topic
- Low-rank approximation theory (142 papers)
- Matrix completion and factorization (118 papers)
- Randomized sketching for matrices (96 papers)
- Structured low-rank learning (87 papers)
- Geometry of low-rank and SPD structure (71 papers)
- Tensor network decompositions (45 papers)
- Low-rank tensor completion (45 papers)
- Randomized tensor decomposition algorithms (43 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).