Book Description

In the presence of data and computational resources, machine learning can be used to synthesize software automatically. For example, machines are now capable of learning complicated pattern recognition tasks and sophisticated decision policies, two key capabilities in autonomous cyber-physical systems. Unfortunately, humans find software synthesized by machine learning algorithms difficult to interpret, which currently limits their use in safety-critical applications such as medical diagnosis and avionic systems. In particular, successful deployments of safety-critical systems mandate the execution of rigorous verification activities, which often rely on human insights, e.g., to identify scenarios in which the system shall be tested. A natural pathway towards a viable verification strategy for such systems is to leverage formal verification techniques, which, in the presence of a formal specification, can provide definitive guarantees with little human intervention. However, formal verification suffers from scalability issues with respect to system complexity. In this thesis, we investigate the limits of current formal verification techniques when applied to a class of machine learning models called tree ensembles, and identify model-specific characteristics that can be exploited to improve the performance of verification algorithms when applied specifically to tree ensembles. To this end, we develop two formal verification techniques specifically for tree ensembles, one fast and conservative technique, and one exact but more computationally demanding. We then combine these two techniques into an abstraction-refinement approach, that we implement in a tool called VoTE (Verifier of Tree Ensembles). Using a couple of case studies, we recognize that sets of inputs that lead to the same system behavior can be captured precisely as hyperrectangles, which enables tractable enumeration of input-output mappings when the input dimension is low. Tree ensembles with a high-dimensional input domain, however, seems generally difficult to verify. In some cases though, conservative approximations of input-output mappings can greatly improve performance. This is demonstrated in a digit recognition case study, where we assess the robustness of classifiers when confronted with additive noise.