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We propose a convex, penalized estimation framework that is particularly well suited to high-dimensional sparse additive models and combines the appealing features of finite basis representation and smoothing penalties. In the case of additive models, a finite basis representation provides a parsimonious representation for fitted functions but is not adaptive when component functions possess different levels of complexity. In contrast, a smoothing spline-type penalty on the component functions is adaptive but does not provide a parsimonious representation. Our proposal simultaneously achieves parsimony and adaptivity in a computationally efficient way. We demonstrate these properties through empirical studies and show that our estimator converges at the minimax rate for functions within a hierarchical class. We further establish minimax rates for a large class of sparse additive models. We also develop an efficient algorithm that scales similarly to the lasso with the number of covariates and sample size.<\/jats:p>","DOI":"10.1093\/biomet\/asy056","type":"journal-article","created":{"date-parts":[[2018,10,9]],"date-time":"2018-10-09T11:42:15Z","timestamp":1539085335000},"page":"87-107","source":"Crossref","is-referenced-by-count":6,"title":["Nonparametric regression with adaptive truncation via a convex hierarchical penalty"],"prefix":"10.1093","volume":"106","author":[{"given":"Asad","family":"Haris","sequence":"first","affiliation":[{"name":"Department of Biostatistics, University of Washington, 1705 NE Pacific Street, Seattle, Washington, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali","family":"Shojaie","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Washington, 1705 NE Pacific Street, Seattle, Washington, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Noah","family":"Simon","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Washington, 1705 NE Pacific Street, Seattle, Washington, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,13]]},"reference":[{"key":"2019072306095654800_B1","author":"Arnold","year":"2014","journal-title":"genlasso: Path Algorithm for Generalized Lasso Problems"},{"key":"2019072306095654800_B2","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1007\/s00041-008-9045-x","article-title":"Enhancing sparsity by reweighted \u21131 minimization","volume":"14","author":"Cand\u00e8s","year":"2008","journal-title":"J. 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