Abstract

Non-negative data are commonly encountered in numerous fields, making nonnegative least squares regression (NNLS) a frequently used tool. At least relative to its simplicity, it often performs rather well in practice. Serious doubts about its usefulness arise for modern high-dimensional linear models. Even in this setting- unlike first intuition may suggest -we show that for a broad class of designs, NNLS is resistant to overfitting and works excellently for sparse recovery when combined with thresholding, experimentally even outperforming regularization. Since NNLS also circumvents the delicate choice of a regularization parameter, our findings suggest that NNLS may be the method of choice.