Numerical optimization for the compatibility constant of the lasso
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917363991969792 |
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| author | Hirose, Kei |
| author_facet | Hirose, Kei |
| contents | The compatibility constant plays an important role in evaluating the prediction error of the lasso in high-dimensional settings. However, the computation of the compatibility constant is generally difficult because it is a complicated nonconvex optimization problem. In this study, we present a numerical approach to compute the compatibility constant when the support of true regression coefficients is given. We show that the optimization problem reduces to a quadratic programming (QP) once the signs of the nonzero coefficients are specified. In this case, the compatibility constant can be obtained by solving QPs for all possible sign combinations. We also formulate a mixed-integer QP (MIQP) approach that can be applied when the number of true nonzero coefficients is large. We investigate the finite-sample behavior of the compatibility constant for simulated data under various parameter settings and compare the prediction error with its theoretical upper bound. The behavior of the compatibility constant in finite samples is also investigated through a real data analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical optimization for the compatibility constant of the lasso Hirose, Kei Computation The compatibility constant plays an important role in evaluating the prediction error of the lasso in high-dimensional settings. However, the computation of the compatibility constant is generally difficult because it is a complicated nonconvex optimization problem. In this study, we present a numerical approach to compute the compatibility constant when the support of true regression coefficients is given. We show that the optimization problem reduces to a quadratic programming (QP) once the signs of the nonzero coefficients are specified. In this case, the compatibility constant can be obtained by solving QPs for all possible sign combinations. We also formulate a mixed-integer QP (MIQP) approach that can be applied when the number of true nonzero coefficients is large. We investigate the finite-sample behavior of the compatibility constant for simulated data under various parameter settings and compare the prediction error with its theoretical upper bound. The behavior of the compatibility constant in finite samples is also investigated through a real data analysis. |
| title | Numerical optimization for the compatibility constant of the lasso |
| topic | Computation |
| url | https://arxiv.org/abs/2512.03321 |