Learning Fast Approximations of Sparse Nonlinear Regression
This addresses sparse nonlinear regression, a challenging problem in machine learning, though it appears incremental as it extends existing unfolding techniques to nonlinear cases.
The authors tackled sparse nonlinear regression by introducing NLISTA, a deep unfolding method that achieves linear convergence under suitable conditions and outperforms state-of-the-art methods on synthetic data.
The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for sparse nonlinear regression problems, a similar idea is rarely exploited due to the complexity of nonlinearity. In this work, we bridge this gap by introducing the Nonlinear Learned Iterative Shrinkage Thresholding Algorithm (NLISTA), which can attain a linear convergence under suitable conditions. Experiments on synthetic data corroborate our theoretical results and show our method outperforms state-of-the-art methods.