论文标题
使用I-PRIORS的加性交互建模
Additive interaction modelling using I-priors
论文作者
论文摘要
在文献中，使用花纹或高斯过程回归等方法在文献中广泛研究了具有相互作用的加性回归模型。但是，由于存在许多平滑参数以及缺乏合适的标准，这些方法可能对估计和模型选择构成挑战。我们建议通过将I-Prior方法（Bergsma，2020）扩展到多个协变量来解决这些挑战，这可能是多维的。与其他方法相比，I-Prorior方法具有一些优势，例如高斯过程回归和Tikhonov正则化，无论是理论上还是实际上。特别是，I-Prior是适当的先验，基于最小的假设，得出可允许的后均值，并且可以使用具有简单E和M步骤的EM算法来完成尺度（或平滑）参数的估计。此外，我们引入了与相互作用的模型的简约规范，该规范具有两个好处：（i）它减少了比例参数的数量，从而促进了通过相互作用的模型的估计，并且（ii）它可以基于边际的可能性来启用直接模型选择（与不同相互作用的模型之间）。
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.
