  From self-driving vehicles and back-flipping robots to virtual assistants who
book our next appointment at the hair salon or at that restaurant for dinner -
machine learning systems are becoming increasingly ubiquitous. The main reason
for this is that these methods boast remarkable predictive capabilities.
However, most of these models remain black boxes, meaning that it is very
challenging for humans to follow and understand their intricate inner workings.
Consequently, interpretability has suffered under this ever-increasing
complexity of machine learning models. Especially with regards to new
regulations, such as the General Data Protection Regulation (GDPR), the
necessity for plausibility and verifiability of predictions made by these black
boxes is indispensable. Driven by the needs of industry and practice, the
research community has recognised this interpretability problem and focussed on
developing a growing number of so-called explanation methods over the past few
years. These methods explain individual predictions made by black box machine
learning models and help to recover some of the lost interpretability. With the
proliferation of these explanation methods, it is, however, often unclear,
which explanation method offers a higher explanation quality, or is generally
better-suited for the situation at hand. In this thesis, we thus propose an
axiomatic framework, which allows comparing the quality of different
explanation methods amongst each other. Through experimental validation, we
find that the developed framework is useful to assess the explanation quality
of different explanation methods and reach conclusions that are consistent with
independent research.
