  Today, machine learning (ML) models are increasingly applied in decision
making. This induces an urgent need for quality assurance of ML models with
respect to (often domain-dependent) requirements. Monotonicity is one such
requirement. It specifies a software as 'learned' by an ML algorithm to give an
increasing prediction with the increase of some attribute values. While there
exist multiple ML algorithms for ensuring monotonicity of the generated model,
approaches for checking monotonicity, in particular of black-box models, are
largely lacking. In this work, we propose verification-based testing of
monotonicity, i.e., the formal computation of test inputs on a white-box model
via verification technology, and the automatic inference of this approximating
white-box model from the black-box model under test. On the white-box model,
the space of test inputs can be systematically explored by a directed
computation of test cases. The empirical evaluation on 90 black-box models
shows verification-based testing can outperform adaptive random testing as well
as property-based techniques with respect to effectiveness and efficiency.
