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Spline regression with automatic knot selection

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  • Goepp, Vivien
  • Bouaziz, Olivier
  • Nuel, Grégory

Abstract

Spline regression has proven to be a useful tool for nonparametric regression. The flexibility of this function family is based on basepoints defining shifts in the behavior of the function – called knots. The question of setting the adequate number of knots and their placement is usually overcome by penalizing over the spline's overall smoothness (e.g. P-splines). However, there are areas of application where finding the best knot placement is of interest. A new method is introduced for automatically selecting knots in spline regression. The approach consists in setting many initial knots and fitting the spline regression through a penalized likelihood procedure called adaptive ridge, which discards the least relevant knots. The method – called A-splines, for adaptive splines – compares favorably with other knot selection methods: it runs way faster (∼10 to ∼400 faster) than comparable methods and has close to equal predictive performance. A-splines are applied to both simulated and real datasets.

Suggested Citation

  • Goepp, Vivien & Bouaziz, Olivier & Nuel, Grégory, 2025. "Spline regression with automatic knot selection," Computational Statistics & Data Analysis, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:csdana:v:202:y:2025:i:c:s0167947324001270
    DOI: 10.1016/j.csda.2024.108043
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, January.
    2. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    3. Eilers, Paul H.C. & Currie, Iain D. & Durban, Maria, 2006. "Fast and compact smoothing on large multidimensional grids," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 61-76, January.
    4. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    5. Ralph C A Rippe & Jacqueline J Meulman & Paul H C Eilers, 2012. "Visualization of Genomic Changes by Segmented Smoothing Using an L0 Penalty," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-14, June.
    6. D. G. T. Denison & B. K. Mallick & A. F. M. Smith, 1998. "Automatic Bayesian curve fitting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 333-350.
    7. Florian Frommlet & Grégory Nuel, 2016. "An Adaptive Ridge Procedure for L0 Regularization," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-23, February.
    8. Marx, Brian D. & Eilers, Paul H. C., 1998. "Direct generalized additive modeling with penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 193-209, August.
    9. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    10. Leitenstorfer, Florian & Tutz, Gerhard, 2007. "Knot selection by boosting techniques," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4605-4621, May.
    11. M. P. Wand, 2000. "A Comparison of Regression Spline Smoothing Procedures," Computational Statistics, Springer, vol. 15(4), pages 443-462, December.
    12. Wallstrom, Garrick & Liebner, Jeffrey & Kass, Robert E., 2008. "An Implementation of Bayesian Adaptive Regression Splines (BARS) in C with S and R Wrappers," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 26(i01).
    13. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, January.
    14. C. C. Holmes & B. K. Mallick, 2001. "Bayesian regression with multivariate linear splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 3-17.
    15. Inyoung Kim & Noah D. Cohen & Raymond J. Carroll, 2003. "Semiparametric Regression Splines in Matched Case-Control Studies," Biometrics, The International Biometric Society, vol. 59(4), pages 1158-1169, December.
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