Abstract interpretation of decision tree ensemble classifiers

We study the problem of formally and automatically verifying robustness properties of decision tree ensemble classifiers such as random forests and gradient boosted decision tree models. A recent stream of works showed how ab- stract interpretation, which is ubiquitously used in static pro- gram analysis, can be successfully deployed to formally ver- ify (deep) neural networks. In this work we push forward this line of research by designing a general and principled abstract interpretation-based framework for the formal verification of robustness and stability properties of decision tree ensemble models. Our abstract interpretation-based method may induce complete robustness checks of standard adversarial perturbations and output concrete adversarial attacks. We implemented our abstract verification technique in a tool called silva, which leverages an abstract domain of not necessarily closed real hyperrectangles and is instantiated to verify random forests and gradient boosted decision trees. Our experimental evaluation on the MNIST dataset shows that silva provides a precise and efficient tool which advances the current state of the art in tree ensembles verification.