제목 : Functional Horseshoe Priors for Subspace Shrinkage
연사 : Harvard 대학 신민석 교수
일정 : 3월 13일 화요일 오전 11시
Abstract : We introduce a new shrinkage prior on function spaces, the functional horseshoe prior, that encourages shrinkage towards parametric classes of functions. Unlike ex- isting shrinkage priors for parametric models, the shrinkage acts on the shape of the function rather than sparsity of model parameters. We theoretically exhibit the efficacy of the proposed approach by showing an adaptive posterior concentration property on the function. We show the consistency of the model selection procedure that thresholds the shrinkage parameter of the functional horseshoe prior. We apply the proposed prior to nonparametric additive models. We compare its performance with the procedure based on the standard horseshoe prior and a number of penal- ized likelihood approaches, and the proposed procedure achieves smaller estimation error and more accurate model selection, compared to the other procedures in the considered simulated and real examples. The proposed prior also provides a natu- ral penalization interpretation, and casts light on a new class of penalized likelihood methods.