mlsanityData to 7 Oct 2026

Optimal Rates For Regularization Of Statistical Inverse Learning Problems

arXiv 1604.04054 ↗First posted 14 Apr 2016stat.MLcited by 68

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Abstract (arXiv)

We consider a statistical inverse learning problem, where we observe the image of a function f through a linear operator A at i.i.d. random design points Xi, superposed with an additive noise. The distribution of the design points is unknown and can be very general. We analyze simultaneously the direct (estimation of Af) and the inverse (estimation of f) learning problems. In this general framework, we obtain strong and weak minimax optimal rates of convergence (as the number of observations n grows large) for a large class of spectral regularization methods over regularity classes defined through appropriate source conditions. This improves on or completes previous results obtained in related settings. The optimality of the obtained rates is shown not only in the exponent in n but also in the explicit dependency of the constant factor in the variance of the noise and the radius of the source condition set.

Key facts. Cited by 68 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Apr 2016.

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Citing papers per year: 2021: 10; 2022: 9; 2023: 20; 2024: 15; 2025: 6; 2026: 8.

68 papers.

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  1. 2022Optimal Rates for Regularized Conditional Mean Embedding Learningcited by 50
  2. 2023Generalization Ability of Wide Neural Networks on ℝcited by 28
  3. 2023On the Optimality of Misspecified Spectral Algorithmscited by 28
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  5. 2021Two-layer neural networks with values in a Banach spacecited by 26
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  8. 2023On the Optimality of Misspecified Kernel Ridge Regressioncited by 20
  9. 2023Kernel interpolation generalizes poorlycited by 16
  10. 2022An elementary analysis of ridge regression with random designcited by 15
  11. 2021Learning curves for Gaussian process regression with power-law priors and targetscited by 14
  12. 2024On the Saturation Effect of Kernel Ridge Regressioncited by 12
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  6. 2022Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regressioncited by 8
  7. 2023Nonlinear Meta-Learning Can Guarantee Faster Ratescited by 8
  8. 2023Adaptive learning of density ratios in RKHScited by 8
  9. 2024Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decaycited by 8
  10. 2021Convex regularization in statistical inverse learning problemscited by 7
  11. 2021Data splitting improves statistical performance in overparametrized regimescited by 6
  12. 2023Random Smoothing Regularization in Kernel Gradient Descent Learningcited by 6
  13. 2021Online nonparametric regression with Sobolev kernelscited by 5
  14. 2021Comparing Classes of Estimators: When does Gradient Descent Beat Ridge Regression in Linear Models?cited by 5
  15. 2023Statistical Learning with Sublinear Regret of Propagator Modelscited by 5
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  18. 2024Overcoming Saturation in Density Ratio Estimation by Iterated Regularizationcited by 5
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  21. 2023Local Risk Bounds for Statistical Aggregationcited by 3
  22. 2023Adaptive Parameter Selection for Kernel Ridge Regressioncited by 3
  23. 2024Optimal Rates and Saturation for Noiseless Kernel Ridge Regressioncited by 3
  24. 2024Learning sparsity-promoting regularizers for linear inverse problemscited by 3
  25. 2025Regularized least squares learning with heavy-tailed noise is minimax optimalcited by 3
  26. 2025Learning Curves of Stochastic Gradient Descent in Kernel Regressioncited by 3
  27. 2025Spectral Algorithms in Misspecified Regression: Convergence under Covariate Shiftcited by 3
  28. 2022Optimal Learning Rates for Regularized Least-Squares with a Fourier Capacity Conditioncited by 2
  29. 2024A Lipschitz spaces view of infinitely wide shallow neural networkscited by 2
  30. 2025Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfercited by 2
  31. 2025Random feature approximation for general spectral methodscited by 2
  32. 2021Beyond Tikhonov: Faster Learning with Self-Concordant Losses via Iterative Regularizationcited by 1
  33. 2022Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensionscited by 1
  34. 2023Sketching with Spherical Designs for Noisy Data Fitting on Spherescited by 1
  35. 2023Kernel-based function learning in dynamic and non stationary environmentscited by 1
  36. 2023Learned reconstruction methods for inverse problems: sample error estimatescited by 1
  37. 2023Statistical inverse learning problems with random observationscited by 1
  38. 2024Spectral Algorithms on Manifolds through Diffusioncited by 1

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