Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to introduce flexibility to standard linear regression models, to express "almost linear" behavior for a phenomenon. A need for GAMs often arises also in physical models, where the model given by theory is an approximation of reality, and one wishes to express the coefficients as functions instead of constants. In this paper, we discuss GAMs from the Bayesian perspective, focusing on linear additive models, where the final model can be formulated as a linear-Gaussian system. We discuss Gaussian Processes (GPs) and local basis function approaches for describing the unknown functions in GAMs, and techniques for specifying prior distributions for them, including spatially varying smoothness. GAMs with both univariate and multivariate functions are discussed. Hyperparameter estimation techniques are presented in order to alleviate the tuning problems related to GAM models. Implementations of all the examples discussed in the paper are made available.

翻译：广义加性模型（GAMs）提供了一种将参数化与非参数化（函数逼近）技术相结合的方法，使其成为适用于多种建模问题的灵活工具。例如，GAMs可用于为标准线性回归模型引入灵活性，以表达现象的“近似线性”行为。在物理模型中，当理论模型仅是对现实的一种近似时，GAMs的需求也常常出现，此时希望将系数表示为函数而非常数。本文从贝叶斯视角探讨GAMs，重点关注线性加性模型，其中最终模型可表述为线性-高斯系统。我们讨论了用于描述GAMs中未知函数的高斯过程（GPs）与局部基函数方法，以及为其指定先验分布的技术（包括空间变平滑性）。文中还讨论了包含单变量与多变量函数的GAMs。为缓解与GAM模型相关的调参问题，我们介绍了超参数估计技术。本文所有讨论示例的实现均已公开提供。