Rethinking Hard Thresholding Pursuit: Full Adaptation and Sharp Estimation
| Title: | Rethinking Hard Thresholding Pursuit: Full Adaptation and Sharp Estimation |
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| Authors: | Zhang, Yanhang, Li, Zhifan, Liu, Shixiang, Wang, Xueqin, Yin, Jianxin |
| Publication Year: | 2025 |
| Collection: | Mathematics Statistics |
| Subject Terms: | Mathematics - Statistics Theory |
| More Details: | Hard Thresholding Pursuit (HTP) has aroused increasing attention for its robust theoretical guarantees and impressive numerical performance in non-convex optimization. In this paper, we introduce a novel tuning-free procedure, named Full-Adaptive HTP (FAHTP), that simultaneously adapts to both the unknown sparsity and signal strength of the underlying model. We provide an in-depth analysis of the iterative thresholding dynamics of FAHTP, offering refined theoretical insights. In specific, under the beta-min condition $\min_{i \in S^*}|{\boldsymbol{\beta}}^*_i| \ge C\sigma (\log p/n)^{1/2}$, we show that the FAHTP achieves oracle estimation rate $\sigma (s^*/n)^{1/2}$, highlighting its theoretical superiority over convex competitors such as LASSO and SLOPE, and recovers the true support set exactly. More importantly, even without the beta-min condition, our method achieves a tighter error bound than the classical minimax rate with high probability. The comprehensive numerical experiments substantiate our theoretical findings, underscoring the effectiveness and robustness of the proposed FAHTP. Comment: 26 pages, 6 figures, 1 table |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2501.02554 |
| Accession Number: | edsarx.2501.02554 |
| Database: | arXiv |
| Description not available. |