We consider a declarative framework for machine learning where concepts and hypotheses are defined by formulas of a logic over some "background structure". We show that within this framework, concepts defined by first-order formulas over a background structure of at most polylogarithmic degree can be learned in polylogarithmic time in the "probably approximately correct" learning sense.
Grohe and Ritzert REF showed that first-order formulas are PAC-learnable over background structures of polylogarithmic degree.
Learning first-order definable concepts over structures of small degree
2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
Mathematics Computer Science