Hans Ulrich Simon

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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)
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)
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)
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)