Gaussian Process (GP) models are a class of flexible non-parametric models
that have rich representational power. By using a Gaussian process with
additive structure, complex responses can be modelled whilst retaining
interpretability. Previous work showed that additive Gaussian process models
require high-dimensional interaction terms. We propose the orthogonal additive
kernel (OAK), which imposes an orthogonality constraint on the additive
functions, enabling an identifiable, low-dimensional representation of the
functional relationship. We connect the OAK kernel to functional ANOVA
decomposition, and show improved convergence rates for sparse computation
methods. With only a small number of additive low-dimensional terms, we
demonstrate the OAK model achieves similar or better predictive performance
compared to black-box models, while retaining interpretability.

提出了正交加性核（OAK）来代替传统高维交互项的加性高斯过程（GP）模型，能够实现可识别、低维度表示的功能关系，并展示了其在稀疏计算方法中的改进收敛速度和优越的预测性能。

加法高斯过程再审视

Additive Gaussian Processes Revisited

Models which estimate main effects of individual variables alongside
interaction effects have an identifiability challenge: effects can be freely
moved between main effects and interaction effects without changing the model
prediction. This is a critical problem for interpretability because it permits
"contradictory" models to represent the same function. To solve this problem,
we propose pure interaction effects: variance in the outcome which cannot be
represented by any smaller subset of features. This definition has an
equivalence with the Functional ANOVA decomposition. To compute this
decomposition, we present a fast, exact algorithm that transforms any
piecewise-constant function (such as a tree-based model) into a purified,
canonical representation. We apply this algorithm to Generalized Additive
Models with interactions trained on several datasets and show large disparity,
including contradictions, between the effects before and after purification.
These results underscore the need to specify data distributions and ensure
identifiability before interpreting model parameters.

为解决特征交互作用估计中存在的可辨认性问题，文章提出了纯交互作用的定义，通过提出一种快速、准确的算法，将任何分段常数函数转换为纯粹的、标准化的表示法，结果表明这种算法可以应用到基于多个数据集进行交互式广义可加模型训练的各个领域。