mlsanityData to 7 Oct 2026

Heteroskedastic PCA: Algorithm, Optimality, and Applications

arXiv 1810.08316 ↗First posted 19 Oct 2018math.ST stat.CO stat.MEcited by 33

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Abstract (arXiv)

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance matrix to remove estimation bias due to heteroskedasticity. This procedure is computationally efficient and provably optimal under the generalized spiked covariance model. A key technical step is a deterministic robust perturbation analysis on singular subspaces, which can be of independent interest. The effectiveness of the proposed algorithm is demonstrated in a suite of problems in high-dimensional statistics, including singular value decomposition (SVD) under heteroskedastic noise, Poisson PCA, and SVD for heteroskedastic and incomplete data.

Key facts. Cited by 33 papers in the map (data through 7 Oct 2026). First posted on arXiv 19 Oct 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 7; 2022: 3; 2023: 6; 2024: 10; 2025: 4; 2026: 3.

33 papers.

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  1. 2021The Power of Contrast for Feature Learning: A Theoretical Analysiscited by 53
  2. 2023Understanding Multimodal Contrastive Learning and Incorporating Unpaired Datacited by 43
  3. 2021Inference for Heteroskedastic PCA with Missing Datacited by 21
  4. 2022Subspace Recovery from Heterogeneous Data with Non-isotropic Noisecited by 14
  5. 2024Optimal Differentially Private PCA and Estimation for Spiked Covariance Matricescited by 10
  6. 2021Fundamental limits for rank-one matrix estimation with groupwise heteroskedasticitycited by 8
  7. 2022Estimating Higher-Order Mixed Memberships via the ℓ2,∞ Tensor Perturbation Boundcited by 8
  8. 2023Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCAcited by 7
  9. 2023Safeguarding Data in Multimodal AI: A Differentially Private Approach to CLIP Trainingcited by 7
  10. 2024Optimal Estimation of Shared Singular Subspaces across Multiple Noisy Matricescited by 6
  11. 2024Matrix Denoising with Doubly Heteroscedastic Noise: Fundamental Limits and Optimal Spectral Methodscited by 5
  12. 2024High-dimensional analysis of ridge regression for non-identically distributed data with a variance profilecited by 4
21 more
  1. 2021Self-Supervised Metric Learning in Multi-View Data: A Downstream Task Perspectivecited by 3
  2. 2024LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimationcited by 3
  3. 2022Treatment Effect Estimation with Unobserved and Heterogeneous Confounding Variablescited by 2
  4. 2023ALPCAH: Sample-wise Heteroscedastic PCA with Tail Singular Value Regularizationcited by 2
  5. 2023Optimal vintage factor analysis with deflation varimaxcited by 2
  6. 2024Contrastive Learning on Multimodal Analysis of Electronic Health Recordscited by 2
  7. 2025ALPCAH: Subspace Learning for Sample-wise Heteroscedastic Datacited by 2
  8. 2021Minimax Estimation of Linear Functions of Eigenvectors in the Face of Small Eigen-Gapscited by 1
  9. 2021Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodescited by 1
  10. 2021Uncertainty Quantification For Low-Rank Matrix Completion With Heterogeneous and Sub-Exponential Noisecited by 1
  11. 2023Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Modelcited by 1
  12. 2025ALPCAHUS: Subspace Clustering for Heteroscedastic Datacited by 1
  13. 2024On Minimum Trace Factor Analysis -- An Old Song Sung to a New Tunecited by 0
  14. 2024Bias-Corrected Joint Spectral Embedding for Multilayer Networks with Invariant Subspace: Entrywise Eigenvector Perturbation and Inferencecited by 0
  15. 2024Statistical Inference in Tensor Completion: Optimal Uncertainty Quantification and Statistical-to-Computational Gapscited by 0
  16. 2024Feature Selection for Latent Factor Modelscited by 0
  17. 2025Subspace Recovery in Winsorized PCA: Insights into Accuracy and Robustnesscited by 0
  18. 2025T-Rex: Fitting a Robust Factor Model via Expectation-Maximizationcited by 0
  19. 2026Adjacency Spectral Embeddings of Correlation Networkscited by 0
  20. 2026Diagonal Attenuation: A Finite-Sample Correction for PCAcited by 0
  21. 2026Heteroskedastic Canonical Polyadic Tensor Decompositioncited by 0