Recovering pairwise interactions, i.e. pairs of input features whose joint effect on an output is different from the sum of their marginal effects, is central in many scientific applications. We conceptualize a solution to this problem as a two-stage procedure: first, we model the relationship between the features and the output using a flexible hybrid neural network; second, we detect feature interactions from the trained model. For the second step we propose a simple and intuitive interaction measure (IM), which has no specific requirements on the machine learning model used in the first step, only that it defines a mapping from an input to an output. And in a special case it reduces to the averaged Hessian of the input-output mapping. Importantly, our method upper bounds the interaction recovery error with the error of the learning model, which ensures that we can improve the recovered interactions by training a more accurate model. We present analyses of simulated and real-world data which demonstrate the benefits of our method compared to available alternatives, and theoretically analyse its properties and relation to other methods.

提出了一种探测未知形式交互作用效应的非参数概率方法，首先用贝叶斯神经网络模拟特征和输出之间的关系，使用Bayesian Group Expected Hessian方法评估交互作用效应和不确定性，最后演示了该方法探测深层神经网络的高阶特征的能力。

使用贝叶斯神经网络学习全局成对交互