mlsanityData to 7 Oct 2026

HARFE: Hard-Ridge Random Feature Expansion

arXiv 2202.02877 ↗First posted 6 Feb 2022stat.ML cs.LG math.OCcited by 12

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Abstract (arXiv)

We propose a random feature model for approximating high-dimensional sparse additive functions called the hard-ridge random feature expansion method (HARFE). This method utilizes a hard-thresholding pursuit-based algorithm applied to the sparse ridge regression (SRR) problem to approximate the coefficients with respect to the random feature matrix. The SRR formulation balances between obtaining sparse models that use fewer terms in their representation and ridge-based smoothing that tend to be robust to noise and outliers. In addition, we use a random sparse connectivity pattern in the random feature matrix to match the additive function assumption. We prove that the HARFE method is guaranteed to converge with a given error bound depending on the noise and the parameters of the sparse ridge regression model. Based on numerical results on synthetic data as well as on real datasets, the HARFE approach obtains lower (or comparable) error than other state-of-the-art algorithms.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 24 of its 54 references that are in the map. First posted on arXiv 6 Feb 2022.

Builds on

24 of 54 references.

References · 24

  1. 2018The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networkscited by 2,250
  2. 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 919
  3. 2019Benign Overfitting in Linear Regressioncited by 544
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  7. 2018Just Interpolate: Kernel "Ridgeless" Regression Can Generalizecited by 190
  8. 2016Generalization Properties of Learning with Random Featurescited by 163
  9. 2020Benign overfitting in ridge regressioncited by 152
  10. 2015On the Equivalence between Kernel Quadrature Rules and Random Feature Expansionscited by 136
  11. 2021Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentrationcited by 110
  12. 2018Does data interpolation contradict statistical optimality?cited by 95
12 more
  1. 2020Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don'tcited by 94
  2. 2018Fast Best Subset Selection: Coordinate Descent and Local Combinatorial Optimization Algorithmscited by 52
  3. 2017Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitionscited by 43
  4. 2021Generalization Bounds for Sparse Random Feature Expansionscited by 22
  5. 2017Subset Selection with Shrinkage: Sparse Linear Modeling when the SNR is lowcited by 17
  6. 2021Interpretable Approximation of High-Dimensional Datacited by 10
  7. 2021SHRIMP: Sparser Random Feature Models via Iterative Magnitude Pruningcited by 9
  8. 2016Additive Approximations in High Dimensional Nonparametric Regression via the SALSAcited by 8
  9. 2021Conditioning of Random Feature Matrices: Double Descent and Generalization Errorcited by 7
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Cited by year

Citing papers per year: 2022: 4; 2023: 1; 2024: 4; 2025: 3.

12 papers.

  1. 2022Random Feature Models for Learning Interacting Dynamical Systemscited by 10
  2. 2022Concentration of Random Feature Matrices in High-Dimensionscited by 8
  3. 2022SRMD: Sparse Random Mode Decompositioncited by 6
  4. 2022SPADE4: Sparsity and Delay Embedding based Forecasting of Epidemicscited by 4
  5. 2024Dispersion based Recurrent Neural Network Model for Methane Monitoring in Albertan Tailings Pondscited by 4
  6. 2023Generalization Bound for Diffusion Models using Random Featurescited by 3
  7. 2025Cauchy Random Features for Operator Learning in Sobolev Spacecited by 3
  8. 2024ANOVA-boosting for Random Fourier Featurescited by 2
  9. 2024Generative Feature Training of Thin 2-Layer Networkscited by 2
  10. 2024Differentially Private Random Feature Modelcited by 2
  11. 2025Learning where to learn: Training data distribution optimization for scientific machine learningcited by 1
  12. 2025Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Spacecited by 1