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Efficient least angle regression for identification of linear-in-the-parameters models.

Wanqing Zhao1, Thomas H Beach1, Yacine Rezgui1

  • 1Cardiff School of Engineering, Cardiff University , Cardiff CF24 3AA, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
|March 16, 2017
PubMed
Summary

We developed an efficient least angle regression algorithm for faster model selection in linear models. This method recursively updates variables, avoiding matrix inversions for improved computational efficiency.

Keywords:
computational efficiencyleast angle regressionlinear-in-the-parameters modelsmodel selectionsystem identification

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Area of Science:

  • Statistics
  • Machine Learning

Background:

  • Least angle regression (LAR) is a model selection technique balancing greediness and speed.
  • LAR relates to L1 norm optimization, enhancing generalization by managing prediction variance and model bias.

Purpose of the Study:

  • To propose an efficient least angle regression algorithm for accelerating model selection.
  • The algorithm targets a broad range of linear-in-the-parameters models.

Main Methods:

  • A recursive algorithm that explicitly derives and updates correlations, directions, and variables.
  • Model coefficients are computed post-recursion, eliminating direct matrix inversions.
  • Computational complexity is analyzed against existing methods involving Cholesky decomposition.

Main Results:

  • The proposed algorithm demonstrates significant computational efficiency.
  • Effectiveness, efficiency, and numerical stability are validated through artificial and real-world examples.

Conclusions:

  • The novel recursive least angle regression algorithm offers a computationally efficient approach to model selection.
  • It provides a stable and effective alternative for linear models, outperforming traditional methods.