mlsanityData to 7 Oct 2026

A Unified Framework for Sparse Relaxed Regularized Regression: SR3

arXiv 1807.05411 ↗First posted 14 Jul 2018stat.ML cs.LG math.OCcited by 36

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Abstract (arXiv)

Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications, variable selection, and high-dimensional analysis. We propose a broad framework for sparse relaxed regularized regression, called SR3. The key idea is to solve a relaxation of the regularized problem, which has three advantages over the state-of-the-art: (1) solutions of the relaxed problem are superior with respect to errors, false positives, and conditioning, (2) relaxation allows extremely fast algorithms for both convex and nonconvex formulations, and (3) the methods apply to composite regularizers such as total variation (TV) and its nonconvex variants. We demonstrate the advantages of SR3 (computational efficiency, higher accuracy, faster convergence rates, greater flexibility) across a range of regularized regression problems with synthetic and real data, including applications in compressed sensing, LASSO, matrix completion, TV regularization, and group sparsity. To promote reproducible research, we also provide a companion MATLAB package that implements these examples.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Jul 2018.

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Citing papers per year: 2021: 5; 2022: 4; 2023: 5; 2024: 6; 2025: 10; 2026: 6.

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  1. 2022Learning Sparse Nonlinear Dynamics via Mixed-Integer Optimizationcited by 29
  2. 2022Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constantscited by 24
  3. 2021DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimizationcited by 19
  4. 2023Benchmarking sparse system identification with low-dimensional chaoscited by 19
  5. 2023Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discoverycited by 15
  6. 2024Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy datacited by 15
  7. 2022Noise-aware Physics-informed Machine Learning for Robust PDE Discoverycited by 14
  8. 2023HyperSINDy: Deep Generative Modeling of Nonlinear Stochastic Governing Equationscited by 7
  9. 2024Parametric PDE Control with Deep Reinforcement Learning and Differentiable L0-Sparse Polynomial Policiescited by 7
  10. 2021On Sparse High-Dimensional Graphical Model Learning For Dependent Time Seriescited by 6
  11. 2023Adaptive Uncertainty-Guided Model Selection for Data-Driven PDE Discoverycited by 6
  12. 2024BINDy -- Bayesian identification of nonlinear dynamics with reversible-jump Markov-chain Monte-Carlocited by 6
24 more
  1. 2021Robust Trimmed k-meanscited by 5
  2. 2025Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networkscited by 5
  3. 2022Learning nonparametric ordinary differential equations from noisy datacited by 4
  4. 2024LES-SINDy: Laplace-Enhanced Sparse Identification of Nonlinear Dynamical Systemscited by 4
  5. 2025Discovering equations from data: symbolic regression in dynamical systemscited by 2
  6. 2025Data-driven Discovery of Digital Twins in Biomedical Researchcited by 2
  7. 2026Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offscited by 2
  8. 2021Uncovering Closed-form Governing Equations of Nonlinear Dynamics from Videoscited by 1
  9. 2021Fully differentiable model discoverycited by 1
  10. 2024SINDyG: Sparse Identification of Nonlinear Dynamical Systems from Graph-Structured Data, with Applications to Stuart-Landau Oscillator Networkscited by 1
  11. 2025SODAs: Sparse Optimization for the Discovery of Differential and Algebraic Equationscited by 1
  12. 2025Hybrid Adaptive Modeling in Process Monitoring: Leveraging Sequence Encoders and Physics-Informed Neural Networkscited by 1
  13. 2023Improved identification accuracy in equation learning via comprehensive boldsymbolR2-elimination and Bayesian model selectioncited by 0
  14. 2024Sparse identification of quasipotentials via a combined data-driven methodcited by 0
  15. 2025Enhancing generalizability of model discovery across parameter space with multi-experiment equation learning (ME-EQL)cited by 0
  16. 2025Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structurescited by 0
  17. 2025Probabilistic and nonlinear compressive sensingcited by 0
  18. 2025A joint optimization approach to identifying sparse dynamics using least squares kernel collocationcited by 0
  19. 2025From STLS to Projection-based Dictionary Selection in Sparse Regression for System Identificationcited by 0
  20. 2026SR4-Fit: An Interpretable and Informative Classification Algorithm Applied to Prediction of U.S. House of Representatives Electionscited by 0
  21. 2026Physics-Consistent Diffusion for Efficient Fluid Super-Resolution via Multiscale Residual Correctioncited by 0
  22. 2026When to Retrain after Drift: A Data-Only Test of Post-Drift Data Size Sufficiencycited by 0
  23. 2026From Video-to-PDE: Data-Driven Discovery of Nonlinear Dye Plume Dynamicscited by 0
  24. 2026Freeze, Then Select: Structured Field Adapters and Stability-Validated Weak Selection for PDE Discovery from Sparse Observationscited by 0