mlsanityData to 14 Oct 2026

Vector-Valued Least-Squares Regression under Output Regularity Assumptions

arXiv 2211.08958 ↗First posted 16 Nov 2022stat.ML cs.LGcited by 5

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Abstract (arXiv)

We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in comparison to full-rank method. Our analysis extends the interest of reduced-rank regression beyond the standard low-rank setting to more general output regularity assumptions. We illustrate our theoretical insights on synthetic least-squares problems. Then, we propose a surrogate structured prediction method derived from this reduced-rank method. We assess its benefits on three different problems: image reconstruction, multi-label classification, and metabolite identification.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 12 of its 46 references that are in the map. First posted on arXiv 16 Nov 2022.

Builds on

12 of 46 references.

References · 12

  1. 2016Generalization Properties of Learning with Random Featurescited by 164
  2. 2015Less is More: Nystr"om Computational Regularizationcited by 91
  3. 2015Operator-valued Kernels for Learning from Functional Response Datacited by 60
  4. 2015Structured Prediction Energy Networkscited by 59
  5. 2021Last iterate convergence of SGD for Least-Squares in the Interpolation regimecited by 42
  6. 2020A General Framework for Consistent Structured Prediction with Implicit Loss Embeddingscited by 35
  7. 2016A Consistent Regularization Approach for Structured Predictioncited by 33
  8. 2018A Structured Prediction Approach for Label Rankingcited by 18
  9. 2017Deep Value Networks Learn to Evaluate and Iteratively Refine Structured Outputscited by 12
  10. 2014On the Sample Complexity of Subspace Learningcited by 7
  11. 2019Leveraging Low-Rank Relations Between Surrogate Tasks in Structured Predictioncited by 5
  12. 2013Nonparametric Reduced Rank Regressioncited by 1

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Cited by year

Citing papers per year: 2023: 4; 2024: 0; 2025: 1.

5 papers.

  1. 2023Sketch In, Sketch Out: Accelerating both Learning and Inference for Structured Prediction with Kernelscited by 5
  2. 2023A randomized algorithm to solve reduced rank operator regressioncited by 4
  3. 2023Recursive Estimation of Conditional Kernel Mean Embeddingscited by 1
  4. 2023Scalable variable selection for two-view learning tasks with projection operatorscited by 1
  5. 2025A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learningcited by 1