{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:02:21Z","timestamp":1760234541993,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,5,22]],"date-time":"2021-05-22T00:00:00Z","timestamp":1621641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Fundamental Research Funds for the Central Universities","award":["2662019FW003","2662020LXQD001"],"award-info":[{"award-number":["2662019FW003","2662020LXQD001"]}]},{"name":"National Natural Science Foundation of China","award":["12001217"],"award-info":[{"award-number":["12001217"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Due to their flexibility and interpretability, additive models are powerful tools for high-dimensional mean regression and variable selection. However, the least-squares loss-based mean regression models suffer from sensitivity to non-Gaussian noises, and there is also a need to improve the model\u2019s robustness. This paper considers the estimation and variable selection via modal regression in reproducing kernel Hilbert spaces (RKHSs). Based on the mode-induced metric and two-fold Lasso-type regularizer, we proposed a sparse modal regression algorithm and gave the excess generalization error. The experimental results demonstrated the effectiveness of the proposed model.<\/jats:p>","DOI":"10.3390\/e23060651","type":"journal-article","created":{"date-parts":[[2021,5,23]],"date-time":"2021-05-23T23:58:05Z","timestamp":1621814285000},"page":"651","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Error Bound of Mode-Based Additive Models"],"prefix":"10.3390","volume":"23","author":[{"given":"Hao","family":"Deng","sequence":"first","affiliation":[{"name":"College of Science, Huazhong Agricultural University, Wuhan 430070, China"}]},{"given":"Jianghong","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Electrical and New Energy, China Three Gorges University, Yichang 443002, China"}]},{"given":"Biqin","family":"Song","sequence":"additional","affiliation":[{"name":"College of Science, Huazhong Agricultural University, Wuhan 430070, China"}]},{"given":"Zhibin","family":"Pan","sequence":"additional","affiliation":[{"name":"College of Science, Huazhong Agricultural University, Wuhan 430070, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1142\/S0219530520400126","article-title":"Learning Rates for Partially Linear Support Vector Machine in High Dimensions","volume":"19","author":"Xia","year":"2021","journal-title":"Anal. 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