<숙명여자대학교 박세원 교수님 초청 강연 안내>

1. 연사: 숙명여자대학교 박세원 교수님

2. 주제: Bayesian Nonparametric Regression viaOvercomplete Systems of B-spline Bases

3. 일시: 2026년 6월 12일(금) 오후 2시

4. 장소: 사이언스홀(자연대 1호관 100호)

5. 발표 초록 :

Flexible function estimation is a fundamental problem in Bayesian nonparametric regression, particularly when the target function exhibits heterogeneous smoothness, such as smooth regions, jump discontinuities, sharp changes, and local peaks. Lévy Adaptive B-Spline regression (LABS) provides an adaptive modeling framework for such functions by extending Lévy Adaptive Regression Kernels (LARK) with B-spline basis functions as generating kernels.

The LABS model represents an unknown function through an overcomplete system of B-spline bases. By allowing the location, scale, coefficient, and degree of each basis function to vary, LABS can adapt to both globally smooth patterns and locally irregular structures. This flexibility makes the model suitable for estimating functions with spatially varying smoothness.

Posterior inference for LABS is developed under a Bayesian framework, and its empirical performance is examined through simulation studies and real data examples. The connection between LABS and Besov function spaces is also discussed to provide insight into how the degree of the B-spline basis relates to the smoothness of the estimated function. In addition, Multivariate Lévy Adaptive B-Spline regression (MLABS) extends LABS to multivariate regression problems by using tensor-product B-spline bases. Empirical results show that LABS and MLABS provide flexible and stable predictive performance for regression problems with complex local structures.