A Fast Coordinate Descent Method for High-Dimensional Non-Negative Least Squares using a Unified Sparse Regression Framework
Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Yang, James, Hastie, Trevor
Institution: Stanford University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403885573