  Neural networks have proven to be effective at solving machine learning tasks
but it is unclear whether they learn any relevant causal relationships, while
their black-box nature makes it difficult for modellers to understand and debug
them. We propose a novel method overcoming these issues by allowing a two-way
interaction whereby neural-network-empowered machines can expose the
underpinning learnt causal graphs and humans can contest the machines by
modifying the causal graphs before re-injecting them into the machines. The
learnt models are guaranteed to conform to the graphs and adhere to expert
knowledge, some of which can also be given up-front. By building a window into
the model behaviour and enabling knowledge injection, our method allows
practitioners to debug networks based on the causal structure discovered from
the data and underpinning the predictions. Experiments with real and synthetic
tabular data show that our method improves predictive performance up to 2.4x
while producing parsimonious networks, up to 7x smaller in the input layer,
compared to SOTA regularised networks.
