A Fast Coordinate Descent Method for High-Dimensional Non-Negative Least Squares using a Unified Sparse Regression Framework
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910672114155520 |
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| author | Yang, James Hastie, Trevor |
| author_facet | Yang, James Hastie, Trevor |
| contents | We develop theoretical results that establish a connection across various regression methods such as the non-negative least squares, bounded variable least squares, simplex constrained least squares, and lasso. In particular, we show in general that a polyhedron constrained least squares problem admits a locally unique sparse solution in high dimensions. We demonstrate the power of our result by concretely quantifying the sparsity level for the aforementioned methods. Furthermore, we propose a novel coordinate descent based solver for NNLS in high dimensions using our theoretical result as motivation. We show through simulated data and a real data example that our solver achieves at least a 5x speed-up from the state-of-the-art solvers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Fast Coordinate Descent Method for High-Dimensional Non-Negative Least Squares using a Unified Sparse Regression Framework Yang, James Hastie, Trevor Computation Statistics Theory We develop theoretical results that establish a connection across various regression methods such as the non-negative least squares, bounded variable least squares, simplex constrained least squares, and lasso. In particular, we show in general that a polyhedron constrained least squares problem admits a locally unique sparse solution in high dimensions. We demonstrate the power of our result by concretely quantifying the sparsity level for the aforementioned methods. Furthermore, we propose a novel coordinate descent based solver for NNLS in high dimensions using our theoretical result as motivation. We show through simulated data and a real data example that our solver achieves at least a 5x speed-up from the state-of-the-art solvers. |
| title | A Fast Coordinate Descent Method for High-Dimensional Non-Negative Least Squares using a Unified Sparse Regression Framework |
| topic | Computation Statistics Theory |
| url | https://arxiv.org/abs/2410.03014 |