Functional Horseshoe Priors for Subspace Shrinkage

• 成果类型: Article
• 署名作者: Shin, Minsuk; Bhattacharya, Anirban; Johnson, Valen E.
• 署名单位: University of South Carolina System; University of South Carolina Columbia; Texas A&M University System; Texas A&M University College Station
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1654875
• 发表日期: 2020
• 页码: 1784-1797
• 关键词: CONVERGENCE-RATES; regression; selection; distributions

摘要

We introduce a new shrinkage prior on function spaces, called the functional horseshoe (fHS) prior, that encourages shrinkage toward parametric classes of functions. Unlike other shrinkage priors for parametric models, the fHS shrinkage acts on the shape of the function rather than inducing sparsity on model parameters. We study the efficacy of the proposed approach by showing an adaptive posterior concentration property on the function. We also demonstrate consistency of the model selection procedure that thresholds the shrinkage parameter of the fHS prior. We apply the fHS prior to nonparametric additive models and compare its performance with procedures based on the standard horseshoe prior and several penalized likelihood approaches. We find that the new procedure achieves smaller estimation error and more accurate model selection than other procedures in several simulated and real examples. for this article, which contain additional simulated and real data examples, MCMC diagnostics, and proofs of the theoretical results, are available online.