Research map / Learning theory and algorithms / Matrix and tensor methods
Sparse regression with guarantees
Recovers sparse signals through hard thresholding, group sparsity and robust estimation with statistical guarantees.
94 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 7 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 8.1% to 3.8%.
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 · PD-Sparse : A Primal and Dual Sparse Approach to Extreme Multiclass and Multilabel Classification (ICML 2016 · 130 citations)
- 2017 · Learning Sparse Task Relations in Multi-Task Learning (AAAI 2017 · 59 citations)
- 2018 · SC2Net: Sparse LSTMs for Sparse Coding (AAAI 2018 · 51 citations)
- 2019 · Large-Scale Sparse Kernel Canonical Correlation Analysis (ICML 2019 · 23 citations)
- 2020 · Sparse Coding with Gated Learned ISTA (ICLR 2020 · 19 citations)
- 2021 · Learned Extragradient ISTA with Interpretable Residual Structures for Sparse Coding (AAAI 2021 · 16 citations)
- 2022 · Unrolling PALM for Sparse Semi-Blind Source Separation (ICLR 2022 · 0 citations)
- 2023 · Global Identifiability of $\ell_1$-based Dictionary Learning via Matrix Volume Optimization (NeurIPS 2023 · 1 citation)
- 2024 · Secure Distributed Sparse Gaussian Process Models Using Multi-Key Homomorphic Encryption (AAAI 2024 · 4 citations)
- 2025 · Foundations of Top-$k$ Decoding for Language Models (NeurIPS 2025 · 0 citations)
- 2026 · Toward Identifiable Sparse Autoencoders (ICML 2026 · 0 citations)
Earliest papers here
- PD-Sparse : A Primal and Dual Sparse Approach to Extreme Multiclass and Multilabel Classification (ICML 2016 · 130 citations)
- Equiangular Kernel Dictionary Learning With Applications to Dynamic Texture Analysis (CVPR 2016 · 43 citations)
- Selective inference for group-sparse linear models (NeurIPS 2016 · 34 citations)
What has been tried
80 papers here report 604 measured changes (a component added, removed or swapped, compared with a baseline): helped 68%, no clear effect 10%, hurt 17%, 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 |
|---|---|---|---|---|
| Increase support set size | Sarcos, PowCons, and SGEMM · RMSE | Helped | Secure Distributed Sparse Gaussian Process Models Using Multi-Key Homomorphic Encryption (AAAI 2024 · 4 citations) | |
| Add diversified correlation using weak constraints | Synthetic block-sparse recovery · NMSE | Helped | Block Sparse Bayesian Learning: A Diversified Scheme (NeurIPS 2024 · 2 citations) | |
| Compress data to 1% of original dimension | Solid-state selective laser sintering · MSE | No clear effect | Efficient Learning of PDEs via Taylor Expansion and Sparse Decomposition into Value and Fourier Domains (AAAI 2024 · 1 citation) | |
| Increase I-OBS pruning iterations from 1 to 75 | ImageNet validation · Top-1 accuracy | 62.98 -> 64.13 | Helped | The Iterative Optimal Brain Surgeon: Faster Sparse Recovery by Leveraging Second-Order Information (NeurIPS 2024 · 0 citations) |
Recent preprints
Loading recent arXiv preprints…
Who publishes on it
Institutions on the most papers of this approach since 2023 (of 21 papers; from OpenAlex and the papers' affiliations).
- Carnegie Mellon University · 3 papers
- Huazhong University of Science and Technology · 2 papers
Use it
Download BibTeX of 36 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 estimation theory (89 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).