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Algorithms for Fitting the Constrained Lasso.

Brian R Gaines1, Juhyun Kim2, Hua Zhou2

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Summary
This summary is machine-generated.

We compared computing strategies for the constrained lasso problem, finding efficient methods applicable to generalized lasso problems. Practical recommendations are provided for various data sizes, with freely available code.

Keywords:
Alternating direction method of multipliersConvex optimizationGeneralized lassoLinear constraintsPenalized regressionRegularization path

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Area of Science:

  • Statistics
  • Computational Mathematics
  • Machine Learning

Background:

  • The constrained lasso problem extends the standard lasso by incorporating linear constraints.
  • These constraints allow users to integrate prior information into statistical models.
  • Efficient algorithms are crucial for solving these problems, especially with large datasets.

Purpose of the Study:

  • To compare alternative computational strategies for solving the constrained lasso problem.
  • To provide practical recommendations on algorithm efficiency and accuracy for different data scales.
  • To demonstrate the applicability of these methods to the generalized lasso problem.

Main Methods:

  • Quadratic programming
  • Alternating Direction Method of Multipliers (ADMM)
  • Development of an efficient solution path algorithm

Main Results:

  • Comparative analysis of algorithms through simulations and benchmark data.
  • Identification of optimal algorithms based on data size, efficiency, and accuracy.
  • Demonstration that generalized lasso can be transformed into a constrained lasso problem.

Conclusions:

  • The developed methods offer efficient solutions for constrained and generalized lasso problems.
  • Practical guidance is provided for selecting appropriate algorithms.
  • The study contributes to the field of penalized regression with accessible code implementations.