Research map / Learning theory and algorithms / Sample complexity
Density and property estimation
Studies maximum likelihood and profile-likelihood estimators for density, mixtures and distribution properties.
86 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.
15 papers in 2023–24 and 16 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic held steady, from 4.5% to 4.9%.
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 · Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences (NeurIPS 2016 · 95 citations)
- 2017 · Fast Fourier Color Constancy (CVPR 2017 · 214 citations)
- 2018 · An Efficient and Provable Approach for Mixture Proportion Estimation Using Linear Independence Assumption (CVPR 2018 · 44 citations)
- 2019 · Uniform Convergence Rate of the Kernel Density Estimator Adaptive to Intrinsic Volume Dimension (ICML 2019 · 13 citations)
- 2020 · Quantum Expectation-Maximization for Gaussian mixture models (ICML 2020 · 13 citations)
- 2021 · Almost Linear Time Density Level Set Estimation via DBSCAN (AAAI 2021 · 8 citations)
- 2022 · Robust Kernel Density Estimation with Median-of-Means principle (ICML 2022 · 8 citations)
- 2023 · Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data (ICML 2023 · 8 citations)
- 2024 · Bagged Deep Image Prior for Recovering Images in the Presence of Speckle Noise (ICML 2024 · 1 citation)
- 2025 · Image Reconstruction from Readout-Multiplexed Single-Photon Detector Arrays (CVPR 2025 · 1 citation)
- 2026 · Approximating f -Divergences with Rank Statistics (ICML 2026 · 0 citations)
Earliest papers here
- Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences (NeurIPS 2016 · 95 citations)
- Mixture Proportion Estimation via Kernel Embeddings of Distributions (ICML 2016 · 87 citations)
- Linking losses for density ratio and class-probability estimation (ICML 2016 · 30 citations)
What has been tried
67 papers here report 416 measured changes (a component added, removed or swapped, compared with a baseline): helped 60%, no clear effect 14%, hurt 18%, mixed 9%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| model up to 3-photon coincidences instead of up to 2-photon coincidences | 2×2 array, optimal mean PPF · PSNR | 23.83 dB -> 24.60 dB | Helped | Image Reconstruction from Readout-Multiplexed Single-Photon Detector Arrays (CVPR 2025 · 1 citation) |
| Remove early stopping by setting t_0 = 0 | Score function at t = 0 · score estimation error | Hurt | Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions (ICML 2024 · 1 citation) | |
| remove the Gaussian-noise correction from the independence score | Bernoulli(p), scaled κ4 = 0 · Amari error | 0.023 -> 0.0419 | Hurt | Nonparametric Evaluation of Noisy ICA Solutions (NeurIPS 2024 · 1 citation) |
| Add iterated regularization to Exp | Geometric Figures (Avg.) · twice Bregman divergence error | 18.775(± 0.123) -> 12.890(± 0.032) | Helped | Overcoming Saturation in Density Ratio Estimation by Iterated Regularization (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 31 papers; from OpenAlex and the papers' affiliations).
- Boston University · 2 papers
- Massachusetts Institute of Technology · 2 papers
- Columbia University · 2 papers
- University of Texas, Austin · 2 papers
- University of Texas at Austin · 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
- Minimax estimation rates (109 papers)
- Optimal mean estimation and subsampling (95 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).