Learning Fast Approximations of Sparse Nonlinear Regression
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.
Code (1)
Tasks
regressionSimilar Papers 제목 키워드 기반
Fast Gaussian Process Approximations for Autocorrelated Data
This paper is concerned with the problem of how to speed up computation for Gaussian process models trained on autocorrelated data. The Gaussian process model is a powerful tool commonly used in nonlinear regression appl…
syren-halofit: A fast, interpretable, high-precision formula for the $Λ$CDM nonlinear matter power spectrum
Rapid and accurate evaluation of the nonlinear matter power spectrum, $P(k)$, as a function of cosmological parameters and redshift is of fundamental importance in cosmology. Analytic approximations provide an interpreta…
regressionSymbolic RegressionNeuronal Gaussian Process Regression
The brain takes uncertainty intrinsic to our world into account. For example, associating spatial locations with rewards requires to predict not only expected reward at new spatial locations but also its uncertainty to a…
regressionOKRidge: Scalable Optimal k-Sparse Ridge Regression
We consider an important problem in scientific discovery, namely identifying sparse governing equations for nonlinear dynamical systems. This involves solving sparse ridge regression problems to provable optimality in or…
regressionscientific discoveryNonlinearities in Macroeconomic Tail Risk through the Lens of Big Data Quantile Regressions
Modeling and predicting extreme movements in GDP is notoriously difficult and the selection of appropriate covariates and/or possible forms of nonlinearities are key in obtaining precise forecasts. In this paper, our foc…
Gaussian Processesquantile regression