mlsanityData to 7 Oct 2026

Efficient Statistics, in High Dimensions, from Truncated Samples

arXiv 1809.03986 ↗First posted 11 Sep 2018math.ST cs.DS cs.LGcited by 28

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Abstract (arXiv)

We provide an efficient algorithm for the classical problem, going back to Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples. Truncated samples from a d-variate normal cal N(μ,Sigma) means a samples is only revealed if it falls in some subset S subseteq ℝd; otherwise the samples are hidden and their count in proportion to the revealed samples is also hidden. We show that the mean μ and covariance matrix Sigma can be estimated with arbitrary accuracy in polynomial-time, as long as we have oracle access to S, and S has non-trivial measure under the unknown d-variate normal distribution. Additionally we show that without oracle access to S, any non-trivial estimation is impossible.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Sep 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 4; 2023: 5; 2024: 4; 2025: 8; 2026: 4.

28 papers.

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  1. 2021Efficient Algorithms for Learning from Coarse Labelscited by 21
  2. 2022Understanding Adversarial Robustness Against On-manifold Adversarial Examplescited by 12
  3. 2021A Computationally Efficient Method for Learning Exponential Family Distributionscited by 10
  4. 2022Efficient Truncated Linear Regression with Unknown Noise Variancecited by 10
  5. 2021Learning from Censored and Dependent Data: The case of Linear Dynamicscited by 9
  6. 2022What Makes A Good Fisherman? Linear Regression under Self-Selection Biascited by 7
  7. 2023Learning Hard-Constrained Models with One Samplecited by 7
  8. 2025The Power of Iterative Filtering for Supervised Learning with (Heavy) Contaminationcited by 7
  9. 2022Perfect Sampling from Pairwise Comparisonscited by 6
  10. 2024Statistical Query Lower Bounds for Learning Truncated Gaussianscited by 6
  11. 2024Transfer Learning Beyond Bounded Density Ratioscited by 6
  12. 2024Efficient Statistics With Unknown Truncation, Polynomial Time Algorithms, Beyond Gaussianscited by 6
16 more
  1. 2023Finite-Sample Symmetric Mean Estimation with Fisher Information Ratecited by 5
  2. 2023Learning Thresholds with Latent Values and Censored Feedbackcited by 3
  3. 2024Unraveling overoptimism and publication bias in ML-driven sciencecited by 3
  4. 2023Learning Mixtures of Gaussians with Censored Datacited by 2
  5. 2023On Computationally Efficient Learning of Exponential Family Distributionscited by 2
  6. 2025Smoothed Analysis of Learning from Positive Samplescited by 2
  7. 2025Learning High-dimensional Gaussians from Censored Datacited by 1
  8. 2025Private Statistical Estimation via Truncationcited by 1
  9. 2025An Optimized Franz-Parisi Criterion and its Equivalence with SQ Lower Boundscited by 1
  10. 2025Linear Regression under Missing or Corrupted Coordinatescited by 1
  11. 2025Learning the Inverse Temperature of Ising Models under Hard Constraints using One Samplecited by 1
  12. 2025Cost Efficient Fairness Audit Under Partial Feedbackcited by 0
  13. 2026Mean Estimation from Coarse Data: Characterizations and Efficient Algorithmscited by 0
  14. 2026High-Dimensional Gaussian Mean Estimation under Realizable Contaminationcited by 0
  15. 2026Mean Testing under Truncation beyond Gaussiancited by 0
  16. 2026Efficient Learning of Truncated Boolean Product Distributions: Influence to the Rescuecited by 0