# Provable Guarantees on the Robustness of Decision Rules to Causal Interventions

arXiv: https://arxiv.org/abs/2105.09108 · HTML: https://mlsanity.com/paper/2105.09108/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 19 May 2021.

## Builds on (most cited first, 8 of 8)

- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [A Differential Approach to Inference in Bayesian Networks](https://mlsanity.com/paper/1301.3847/) (2013)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [Verifying Properties of Binarized Deep Neural Networks](https://mlsanity.com/paper/1709.06662/) (2017)
- [On Tractable Representations of Binary Neural Networks](https://mlsanity.com/paper/2004.02082/) (2020)
- [On Relaxing Determinism in Arithmetic Circuits](https://mlsanity.com/paper/1708.06846/) (2017)

## Built on by (most cited first, 6 of 6)

- [From Robustness to Explainability and Back Again](https://mlsanity.com/paper/2306.03048/) (2023)
- [Causal Inference Using Tractable Circuits](https://mlsanity.com/paper/2202.02891/) (2022)
- [Compositional Probabilistic and Causal Inference using Tractable Circuit Models](https://mlsanity.com/paper/2304.08278/) (2023)
- [Scaling Probabilistic Circuits via Monarch Matrices](https://mlsanity.com/paper/2506.12383/) (2025)
- [Robustness Guarantees for Credal Bayesian Networks via Constraint Relaxation over Probabilistic Circuits](https://mlsanity.com/paper/2205.05793/) (2022)
- [Bayesian Network Models of Causal Interventions in Healthcare Decision Making: Literature Review and Software Evaluation](https://mlsanity.com/paper/2211.15258/) (2022)

## Abstract (arXiv)

Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical) changes in the data-generating process, whether due to natural reasons or by the action of an adversary. We consider causal Bayesian networks and formally define the interventional robustness problem, a novel model-based notion of robustness for decision functions that measures worst-case performance with respect to a set of interventions that denote changes to parameters and/or causal influences. By relying on a tractable representation of Bayesian networks as arithmetic circuits, we provide efficient algorithms for computing guaranteed upper and lower bounds on the interventional robustness probabilities. Experimental results demonstrate that the methods yield useful and interpretable bounds for a range of practical networks, paving the way towards provably causally robust decision-making systems.