mlsanityData to 14 Oct 2026

Generalized Eigenvalue Problems with Generative Priors

arXiv 2411.01326 ↗First posted 2 Nov 2024cs.LG stat.MLcited by 3

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Abstract (arXiv)

Generalized eigenvalue problems (GEPs) find applications in various fields of science and engineering. For example, principal component analysis, Fisher's discriminant analysis, and canonical correlation analysis are specific instances of GEPs and are widely used in statistical data processing. In this work, we study GEPs under generative priors, assuming that the underlying leading generalized eigenvector lies within the range of a Lipschitz continuous generative model. Under appropriate conditions, we show that any optimal solution to the corresponding optimization problems attains the optimal statistical rate. Moreover, from a computational perspective, we propose an iterative algorithm called the Projected Rayleigh Flow Method (PRFM) to approximate the optimal solution. We theoretically demonstrate that under suitable assumptions, PRFM converges linearly to an estimated vector that achieves the optimal statistical rate. Numerical results are provided to demonstrate the effectiveness of the proposed method.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 34 of its 97 references that are in the map. First posted on arXiv 2 Nov 2024.

Builds on

34 of 97 references.

References · 34

  1. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  2. 2017Compressed Sensing using Generative Modelscited by 339
  3. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 291
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  11. 2019Algorithmic Guarantees for Inverse Imaging with Untrained Network Priorscited by 32
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22 more
  1. 2014Sparse CCA: Adaptive Estimation and Computational Barrierscited by 25
  2. 2020Sample Complexity Bounds for 1-bit Compressive Sensing and Binary Stable Embeddings with Generative Priorscited by 21
  3. 2019The spiked matrix model with generative priorscited by 20
  4. 2019Exact asymptotics for phase retrieval and compressed sensing with random generative priorscited by 20
  5. 2019Alternating Phase Projected Gradient Descent with Generative Priors for Solving Compressive Phase Retrievalcited by 18
  6. 2020The Generalized Lasso with Nonlinear Observations and Generative Priorscited by 15
  7. 2021Provable Compressed Sensing with Generative Priors via Langevin Dynamicscited by 14
  8. 2021Towards Sample-Optimal Compressive Phase Retrieval with Sparse and Generative Priorscited by 14
  9. 2022Generative Principal Component Analysiscited by 12
  10. 2013Sparse PCA through Low-rank Approximationscited by 11
  11. 2016Efficient Algorithms for Large-scale Generalized Eigenvector Computation and Canonical Correlation Analysiscited by 10
  12. 2016Sparse Generalized Eigenvalue Problem with Application to Canonical Correlation Analysis for Integrative Analysis of Methylation and Gene Expression Datacited by 7
  13. 2022Misspecified Phase Retrieval with Generative Priorscited by 7
  14. 2023A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensingcited by 7
  15. 2014Sparse Generalized Eigenvalue Problem via Smooth Optimizationcited by 6
  16. 2014A Convex Sparse PCA for Feature Analysiscited by 6
  17. 2016Sparse Generalized Eigenvalue Problem: Optimal Statistical Rates via Truncated Rayleigh Flowcited by 6
  18. 2013Optimal Feature Selection in High-Dimensional Discriminant Analysiscited by 4
  19. 2013Sparse CCA via Precision Adjusted Iterative Thresholdingcited by 4
  20. 2017Penalized Orthogonal Iteration for Sparse Estimation of Generalized Eigenvalue Problemcited by 4
  21. 2017The Informativeness of K -Means for Learning Mixture Modelscited by 3
  22. 2020An Inverse-free Truncated Rayleigh-Ritz Method for Sparse Generalized Eigenvalue Problemcited by 2

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Citing papers per year: 2025: 3.

3 papers.

  1. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  2. 2025Learning Single Index Models with Diffusion Priorscited by 2
  3. 2025Diffusion Model Based Signal Recovery Under 1-Bit Quantizationcited by 1