2020/07/30 by Wicher Bergsma, Haziq Jamil, Bergsma, Wicher +1
Computer Science · Decision Sciences · Mathematics · #Additive model #Advanced Statistical Methods and Models #Artificial intelligence #Bayesian probability #Computer science #Covariate #FOS: Computer and information sciences #FOS: Mathematics #Forecasting Techniques and Applications #Gaussian #Gaussian Processes and Bayesian Inference #Gaussian process #Inverse problem #Kriging #Machine Learning (stat.ML) #Machine learning #Mathematical optimization #Mathematics #Methodology (stat.ME) #Model selection #Nonparametric regression #Prior probability #Regression #Regression analysis #Regularization (linguistics) #Scale (ratio) #Selection (genetic algorithm) #Smoothing #Statistics #Statistics Theory (math.ST) #Tikhonov regularization
paper · pdf · doi:10.48550/arxiv.2007.15766
openalex publication_date 2020/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Additive regression models with interactions are widely studied in the literature, using methods such as splines or Gaussian process regression. However, these methods can pose challenges for estimation and model selection, due to the presence of many smoothing parameters and the lack of suitable criteria. We propose to address these challenges by extending the I-prior methodology (Bergsma, 2020) to multiple covariates, which may be multidimensional. The I-prior methodology has some advantages over other methods, such as Gaussian process regression and Tikhonov regularization, both theoretically and practically. In particular, the I-prior is a proper prior, is based on minimal assumptions, yields an admissible posterior mean, and estimation of the scale (or smoothing) parameters can be done using an EM algorithm with simple E and M steps. Moreover, we introduce a parsimonious specification of models with interactions, which has two benefits: (i) it reduces the number of scale parameters and thus facilitates the estimation of models with interactions, and (ii) it enables straightforward model selection (among models with different interactions) based on the marginal likelihood.