Minimizing Disagreements for Geometric Regions Using Dynamic Programming , with Applications to Machine Learning and Computer Graphics

We demonstrate that the dynamic programming paradigm is an eeective tool in the design of eecient algorithms for solving minimumdisagreement problems for convex polygons, star-shaped polygons, unions of axis-parallel boxes and various other classes of geometric regions. In particular, we show that the minimizing disagreement problem for convex k-gons on a sample of size n can be solved in O(n 6 k) time. Together with earlier known results, we obtain algorithms for learning these geometric regions in the agnostic PAC learning model and the PAC model with random classiication noise. Furthermore, these algorithms also allow us to track slowly drifting concept from these geometric regions. Most of these algorithms can be naturally adapted to solve related discrepancy problems that have applications in image compression, geometrical clustering and numerical integration.

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