Judea Pearl’s structural causal models are among the most prominent examples of the mathematical tools that can help us in unraveling the complex causal relationships across data. These models, based on Bayesian networks (see Section 5.5.3) allow to answer more complex queries, like the effect of interventions on some variables and counterfactuals.

In some recent papers, IDSIA researchers identified an equivalence relation between causal models and credal networks, a generalised class of Bayesian networks, on which IDSIA has a long-standing experience. Causal analysis through credal network equivalence appears as a promising research direction worth of investigation in the next years. Vice versa, some new recent algorithms developed for causal queries could be used for credal networks. IDSIA is traditionally using credal networks in a applied projects to model expert knowledge (knowledge engineering), and support or explain the corresponding decisions. It seems possible to develop new approximate techniques for these models and apply them to such problems. Notably the above pieces of theoretical research have been always supported by free software libraries developed by the IDSIA team and implementing the new algorithms. The same is expected to happen for the above considered future work.

## References

- Zaffalon, M., Antonucci, A., & Cabañas, R. (2020). Structural causal models are (solvable by) credal networks. In International Conference on Probabilistic Graphical Models (pp. 581-592). PMLR.
- Cabañas, R., Antonucci, A., Huber, D., & Zaffalon, M. (2020). CREDICI: A Java Library for Causal Inference by Credal Networks. In International Conference on Probabilistic Graphical Models (pp. 597-600). PMLR.
- Zaffalon, M., Antonucci, A., & Cabañas, R. (2020). Causal Expectation Maximisation. arXiv preprint arXiv:2011.02912.