The Effective Number of Nonzeros: Theory and Regularization for Sparse Recovery
Classical sparse recovery treats all nonzero entries equally, though numerical noise often creates long tails of negligible coefficients. This paper develops an entropy-based notion of effective sparsity to measure the coefficients carrying significant mass. The central quantity, the effective number of nonzeros (ENZ), is obtained by exponentiating the Shannon entropy of the normalized magnitude distribution. We show that ENZ decomposes exactly into the support cardinality multiplied by a distributional efficiency factor, thereby making precise its relation to the $\ell_0$ count and explaining how it discounts uninformative coefficients. Furthermore, the Shannon ENZ is embedded into a par...
| Authors | Haoyu He, Hao Wang, Jiashan Wang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 14 March 2026 |
| Last updated at source | 24 June 2026 |
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