  Estimating global pairwise interaction effects, i.e., the difference between
the joint effect and the sum of marginal effects of two input features, with
uncertainty properly quantified, is centrally important in science
applications. We propose a non-parametric probabilistic method for detecting
interaction effects of unknown form. First, the relationship between the
features and the output is modelled using a Bayesian neural network, capable of
representing complex interactions and principled uncertainty. Second,
interaction effects and their uncertainty are estimated from the trained model.
For the second step, we propose an intuitive global interaction measure:
Bayesian Group Expected Hessian (GEH), which aggregates information of local
interactions as captured by the Hessian. GEH provides a natural trade-off
between type I and type II error and, moreover, comes with theoretical
guarantees ensuring that the estimated interaction effects and their
uncertainty can be improved by training a more accurate BNN. The method
empirically outperforms available non-probabilistic alternatives on simulated
and real-world data. Finally, we demonstrate its ability to detect
interpretable interactions between higher-level features (at deeper layers of
the neural network).
