D. Dobkin and D. Gunopulos. Concept Learning with Geometric Hypotheses. in Proc. Conf. on Comp. Learning Theory, pages 329--344, 1995. Home/Search Document Details and Download
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On Simplifying Dot Maps - de Berg, Bose, Chcong, Morin (2002) (1 citation) (Correct)
....set P is identical to finding a subset 62 C P such that the discrepancy of 62 with respect to P and dot value 2 is minimized. The concept of bichromatic discrepancy arises in computational learning theory, in particular in the so called minimizing disagreement problem in agnostic PAC lea.rning [7, 11]. Thus our algorithms to compute the approximation error of two given sets with respect to a family 7g of ranges may be used to solve the minimizing disagreement problem when the class of hypotheses is 7g see the paper by Dobkin et al. 8] for details. Finally, we note that our problem is related ....
D. Dobkin and D. Gunopulos. Concept Learning with Geometric Hypotheses. in Proc. ConJ on Comp. Learning Theory, pages 329 344, 1995.
PAC Learning Intersections of Halfspaces with Membership Queries - Kwek, Pitt (1998) (4 citations) (Correct)
....domain, Ben David et al. 28] give an exact learning algorithm for the same class using equivalence queries only. Recently the more difficult related problem of finding a convex polygon (in the plane) of s sides that misclassifies the fewest number of points in a finite sample has been studied [29, 30, 31]. An O(n 6 k) time algorithm for finding one polygon in the class of convex s gons that minimizes the classification error on a sample of labeled points is given [31] This result implies that convex polygons are learnable in the PAC model with random classification noise [32] and the ....
D. Dobkin and D. Gunopulos. Concept learning with geometric hypotheses. In Proc. 8th Annu. Conf. on Comput. Learning Theory, pages 329--336. ACM Press, New York, NY, 1995.
Geometric Concept Learning and Related Topics - Kwek (1997) (2 citations) (Correct)
....loss functions, depth two neural networks where the hidden nodes are linear threshold gates with constant fan in. Recently the more difficult related problem of finding a convex polygon (in the plane) of k sides that misclassifies the fewest number of points in a finite sample has been studied [DG95, Fis95] However, our result in Section 4.4 is more efficient. These results imply that convex polygons are learnable in the PAC model with random classification noise [AL88] and the agnostic PAC model [KSS94] Learning boxes: There have been a number of papers on learning the boxes. Blumer et ....
....O(n 5 ) time MDP algorithm. Maass [Maa94] improves this trivial time bound to O(n 2 log n) Also, Kearns et al. KSS94] solves the MDP for the class of k piecewise functions over any class of functions F where the MDP for F can be solved in polynomial time in n. Dobkin and Gunopulos [DG95] solve the MDP for planar k stripes in O(k 2 n 2 log(n) time. All these algorithms use the dynamic programming paradigm. Thus, one may wonder if the dynamic programming paradigm can be employed to efficiently minimize disagreement for other more complex geometric regions. 4.2 Defintions and ....
David P. Dobkin and Dimitrios Gunopulos. Concept learning with geometric hypotheses. In Proc. 8th Annu. Conf. on Comput. Learning Theory, pages 329--336. ACM Press, New York, NY, 1995.
Geometric Problems in Machine Learning. - Dobkin, Gunopulos Self-citation (Dobkin Gunopulos) (Correct)
....learners. In this section we present the known results for the minimizing disagreement problem for geometric hypotheses. There has been a lot of theoretical work in computational learning theory on the PAC and agnosticPAC learnability of various hypothesis classes ( KSS] F] K] Ma] [DG]) Unfortunately much of this work is not practical either because of the complexity of the algorithms or because of the inadequate performance of the hypothesis classes. One important aspect of geometric concepts is that they are powerful enough to be useful, yet they are intuitive and simple ....
....algorithm s simplicity allows easy implementation. Experiments also show that it is reasonably fast. Fischer and Kwek ( F] K] consider the problem of computing the optimum k gon in two dimensions (for a fixed k) They give a dynamic algorithm of O(kn 6 ) running time. For the same problem ([DG]) give a different algorithm with a running time of O(n 2k Gamma1 log n) 2.3 Decision trees that minimize the error In this section we are going to consider the hypothesis classes T (1; K) and T (2; K) A decision tree T is in T (2; K) if it has a binary split in one dimension, and a K way ....
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D. Dobkin and D. Gunopulos, Concept Learning with Geometric Hypotheses, 8th ACM Conference on Learning Theory, 1995.
On Simplifying Dot Maps - de Berg, Bose, Cheong, Morin (2003) (1 citation) (Correct)
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D. Dobkin and D. Gunopulos. Concept Learning with Geometric Hypotheses. in Proc. Conf. on Comp. Learning Theory, pages 329--344, 1995.
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