Abstract

We present a general approach to solving the minimizing disagreement problem for geometric hypotheses with finite VC-dimension. These results also imply efficient agnostic-PAC learning of these hypotheses classes. In particular we give an O(n min(ff+1=2;2k01) log n) algorithm that solves the m.d.p. for two-dimensional convex k-gon hypotheses (where ff is the VC dimension of the implied set system, k is constant) , and an O(n 3k01 log n) algorithm for convex k-hedra hypotheses in three dimensions. We extend these results to handle unions of k- gons and give an approach to approximation algorithms. 1 The Minimizing Disagreement Problem An important goal of applied machine learning is to provide tools for the design and analysis of learning algorithms that provide satisfactory solutions for realworld learning problems. There are a lot of experimental results regarding the performance of various heuristic learning algorithms on a number of "benchmark"- datasets for r...

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