Lehrstuhl Mathematik & InformatikHierarchical Design of Fast Minimum Disagreement Algorithms
Abstract. We compose a toolbox for the design of Minimum Disagreement algorithms. This box contains general procedures which transform (without much loss of efficiency) algorithms that are successful for some d-dimensional (geometric) concept class C into algorithms which are successful for a (d+1)-dimensional extension of C . An iterative application of these transformations has the potential of starting with a base algorithm for a trivial problem and ending up at a smart algorithm for a non-trivial problem. In order to make this working, it is essential that the algorithms are not proper, i.e., they return a hypothesis that is not necessarily a member of C. However, the “price” for using a super-class H of C is so low that the resulting time bound for achieving accuracy ε in the model of agnostic learning is significantly smaller than the time bounds achieved by the up-to-date best (proper) algorithms. We evaluate the transformation technique for d=2 on both artificial and real-life data sets and demonstrate that it provides a fast algorithm, which can successfully solve practical problems on large data sets.