Figure 1. Illustration of the construction of counterfactual examples. First a point $x$ is mapped by $f$ into the $Z$-domain. Then the embedding is shifted to the decision boundary, before being mapped back into the $X$-domain.
“How can I make a minimal and realistic change to an input such that the predicted outcome change?” This is the answer which I am aiming to answer using invertible Neural Networks. The idea relates a lot to pre-imaging from, e.g., kernel-methods.
The idea is the followig. Learn a non-linear and invertible transform $f$ on your data. Compose this transform with a linear binary classifier to get a predictive model. From this construction, you can train the composition using, e.g., binary cross-entropy. So produce a counterfactual example, one can then take an embedded feature vector and shift it onto the decision-boundary of the linear classifier before inverting the shifted embedding. The idea is illustrated below.
Figure 1. Illustration of the construction of counterfactual examples. First a point $x$ is mapped by $f$ into the $Z$-domain. Then the embedding is shifted to the decision boundary, before being mapped back into the $X$-domain.
Preliminary experiments on the GLOW network from [1] shows promissing results.
[1] Kingma, D.P. and Dhariwal, P., 2018. Glow: Generative flow with invertible 1x1 convolutions. In Advances in Neural Information Processing Systems (pp. 10215-10224).