Sharp Trade-Offs in High-Dimensional Inference via 2-Level SLOPE
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912478478204928 |
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| author | Bu, Zhiqi Klusowski, Jason M. Rush, Cynthia Wu, Ruijia |
| author_facet | Bu, Zhiqi Klusowski, Jason M. Rush, Cynthia Wu, Ruijia |
| contents | Among techniques for high-dimensional linear regression, Sorted L-One Penalized Estimation (SLOPE) generalizes the LASSO via an adaptive $l_1$ regularization that applies heavier penalties to larger coefficients in the model. To achieve such adaptivity, SLOPE requires the specification of a complex hierarchy of penalties, i.e., a monotone penalty sequence in $R^p$, in contrast to a single penalty scalar for LASSO. Tuning this sequence when $p$ is large poses a challenge, as brute force search over a grid of values is computationally prohibitive. In this work, we study the 2-level SLOPE, an important subclass of SLOPE, with only three hyperparameters. We demonstrate both empirically and analytically that 2-level SLOPE not only preserves the advantages of general SLOPE -- such as improved mean squared error and overcoming the Donoho-Tanner power limit -- but also exhibits computational benefits by reducing the penalty hyperparameter space. In particular, we prove that 2-level SLOPE admits a sharp, theoretically tight characterization of the trade-off between true positive proportion (TPP) and false discovery proportion (FDP), contrasting with general SLOPE where only upper and lower bounds are known. Empirical evaluations further underscore the effectiveness of 2-level SLOPE in settings where predictors exhibit high correlation, when the noise is large, or when the underlying signal is not sparse. Our results suggest that 2-level SLOPE offers a robust, scalable alternative to both LASSO and general SLOPE, making it particularly suited for practical high-dimensional data analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09110 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp Trade-Offs in High-Dimensional Inference via 2-Level SLOPE Bu, Zhiqi Klusowski, Jason M. Rush, Cynthia Wu, Ruijia Methodology Machine Learning Among techniques for high-dimensional linear regression, Sorted L-One Penalized Estimation (SLOPE) generalizes the LASSO via an adaptive $l_1$ regularization that applies heavier penalties to larger coefficients in the model. To achieve such adaptivity, SLOPE requires the specification of a complex hierarchy of penalties, i.e., a monotone penalty sequence in $R^p$, in contrast to a single penalty scalar for LASSO. Tuning this sequence when $p$ is large poses a challenge, as brute force search over a grid of values is computationally prohibitive. In this work, we study the 2-level SLOPE, an important subclass of SLOPE, with only three hyperparameters. We demonstrate both empirically and analytically that 2-level SLOPE not only preserves the advantages of general SLOPE -- such as improved mean squared error and overcoming the Donoho-Tanner power limit -- but also exhibits computational benefits by reducing the penalty hyperparameter space. In particular, we prove that 2-level SLOPE admits a sharp, theoretically tight characterization of the trade-off between true positive proportion (TPP) and false discovery proportion (FDP), contrasting with general SLOPE where only upper and lower bounds are known. Empirical evaluations further underscore the effectiveness of 2-level SLOPE in settings where predictors exhibit high correlation, when the noise is large, or when the underlying signal is not sparse. Our results suggest that 2-level SLOPE offers a robust, scalable alternative to both LASSO and general SLOPE, making it particularly suited for practical high-dimensional data analysis. |
| title | Sharp Trade-Offs in High-Dimensional Inference via 2-Level SLOPE |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2507.09110 |