Property Testing: A Learning Theory Perspective

Property Testing takes the learning-theory point of view of property testing and focuses on results for testing properties of functions that are of interest to the learning theory community. In particular it covers results for testing algebraic properties of functions such as linearity, testing properties defined by concise representations, such as having a small DNF representation, and more. It starts with some preliminaries, including a precise statement and proof of the simple but important observation that testing is no harder than learning. It goes on to consider the first type of properties that were studied in the context of property testing: algebraic properties. These include testing whether a function is (multi-)linear and more generally whether it is a polynomial of bounded degree. It then turns to the study of function class that have a concise (propositional logic) representation such as singletons, monomials and small DNF formula. It proceeds to discuss distribution free testing, and testing from random examples alone. Finally, it contains a brief survey of other results in property testing. These include testing monotonicity, testing of clustering, testing properties of distributions, and more. Property Testing is an ideal text for anybody with an interest in property testing and how it connects to topics in machine learning.