Parameterized Complexity in Machine Learning

Classifying the complexity of problems into those which can be seen as “tractable” and those which are “intractable” has been a core topic of theoretical computer science already since its inception. For the latter class, the parameterized complexity paradigm pioneered by Downey and Fellows provides a powerful set of tools to identify the exact boundaries of tractability for each specific problem under consideration. And yet, in many subfields of machine learning, there has historically been a distinct lack of research targeting the parameterized complexity of fundamental problems.

In this survey, we take aim at some of the recent developments at the interface between machine learning and parameterized complexity which successfully bridge the gap between these two areas of research. The survey focuses primarily on three subfields of machine learning where significant progress towards this direction has been made in recent years: Bayesian Networks, Data Completion and Neural Network Training. The survey also provides pointers to some related developments in other subfields of machine learning, such as Decision Tree Learning and Sample Complexity.