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- Shai Ben-David, Nadav Eiron, Hans Ulrich Simon
- COLT/EuroCOLT
- 2001

The notion of embedding a class of dichotomies in a class of linear half spaces is central to the support vector machines paradigm. We examine the question of determining the minimal Euclidean dimension and the maximal margin that can be obtained when the embedded class has a finite VC dimension. We show that an overwhelming majority of the family of finite… (More)

- Klaus-Uwe Höffgen, Hans Ulrich Simon, Kevin S. Van Horn
- J. Comput. Syst. Sci.
- 1992

We investigate the problem of learning concepts by presenting labeled and randomly chosen training–examples to single neurons. It is well-known that linear halfspaces are learnable by the method of linear programming. The corresponding (Mc-Culloch-Pitts) neurons are therefore efficiently trainable to learn an unknown halfspace from examples. We want… (More)

- Shai Ben-David, Hans Ulrich Simon
- NIPS
- 2000

We consider the existence of efficient algorithms for learning the class of half-spaces in ~n in the agnostic learning model (Le., making no prior assumptions on the example-generating distribution). The resulting combinatorial problem finding the best agreement half-space over an input sample is NP hard to approximate to within some constant factor. We… (More)

- Hans Ulrich Simon
- SIAM J. Discrete Math.
- 1990

- Thomas Hofmeister, Matthias Krause, Hans Ulrich Simon
- COCOON
- 1997

- Nikolas List, Hans Ulrich Simon
- COLT
- 2005

We present a general decomposition algorithm that is uniformly applicable to every (suitably normalized) instance of Convex Quadratic Optimization and efficiently approaches an optimal solution. The number of iterations required to be within ε of optimality grows linearly with 1/ε and quadratically with the number m of variables. The working set selection… (More)

- Bernd Becker, Hans Ulrich Simon
- 27th Annual Symposium on Foundations of Computer…
- 1986

The n-cube network is called faulty if it contains any faulty processor or any faulty link. For any number k we are interested in the minimum number f(n, k) of faults, necessary for an adversary to make any (n-k)-dimensional subcube faulty. Reversely formulated: The existence of a (n-k)- dimensional nonfaulty subcube can be guaranteed, unless there are at… (More)

- Nikolas List, Hans Ulrich Simon
- COLT
- 2004

- Matthias Krause, Hans Ulrich Simon
- Combinatorics, Probability & Computing
- 2000