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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.03014 |
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Table of 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.