B1481
Title: Variational inference for locally shape constrained splines
Authors: Jens Lichter - University of Goettingen (Germany) [presenting]
Thomas Kneib - University of Goettingen (Germany)
Abstract: Generalized additive models have emerged as powerful tools for analyzing complex relationships between predictors and response variables. One reason is the variety of different effect types for the predictors. For instance, linear effects retain easily interpretable results, as opposed to nonlinear effects, which, however, are more flexible and thus capture nonlinear relations. A trade-off between interpretability and flexibility is using nonlinear effects under certain shape constraints. A nonlinear effect can, for example, be constrained to be monotonic, increasing or decreasing. The focus is on shape-constrained P-Splines (SCP-Splines). SCP-Splines are embedded in a Bayesian framework and conduct inference based on mean-field variational inference. Different parameter transformations are proposed under the constraint, and SCP-Splines are further extended to define constraints only locally such that different parts of the predictors are modelled nonlinearly with or without constraints. To evaluate the performance of the proposed approach, a simulation study is conducted and the method is applied to real-world data sets. The findings underline that incorporating shape constraints can significantly enhance model interpretability and predictive accuracy and that the proposed method can outperform existing implementations in accurately capturing the underlying relationships and the uncertainty of the estimates.
