197,125 research outputs found

    The Complexity of Optimizing over a Simplex, Hypercube or Sphere: A Short Survey

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    We consider the computational complexity of optimizing various classes of continuous functions over a simplex, hypercube or sphere.These relatively simple optimization problems have many applications.We review known approximation results as well as negative (inapproximability) results from the recent literature.computational complexity;global optimization;linear and semidefinite programming;approximation algorithms

    A scalable learning algorithm for Kernel Probabilistic Classifier

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    National audienceIn this paper we propose a probabilistic classification algorithm that learns a set of kernel functions that associate a probability distribution over classes to an input vector. This model is obtained by maximizing a measure over the probability distributions through a local optimization process. This measure focuses on the faithfulness of the whole probability distribution induced rather than only considering the probabilities of the classes separately. We show that, thanks to a pre-processing computation, the complexity of the evaluation of this measure with respect to a model is no longer dependent on the size of the training set. This makes the local optimization of the whole set of kernel functions tractable, even for large databases. We experiment our method on five benchmark datasets and the KDD Cup 2012 dataset

    The World of Combinatorial Fuzzy Problems and the Efficiency of Fuzzy Approximation Algorithms

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    We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and produce fuzzy values. To solve such problems efficiently, we design fast fuzzy algorithms, which are modeled by polynomial-time deterministic fuzzy Turing machines equipped with read-only auxiliary tapes and write-only output tapes and also modeled by polynomial-size fuzzy circuits composed of fuzzy gates. We also introduce fuzzy proof verification systems to model the fuzzification of nondeterminism. Those models help us identify four complexity classes: Fuzzy-FPA of fuzzy functions, Fuzzy-PA and Fuzzy-NPA of fuzzy decision problems, and Fuzzy-NPAO of fuzzy optimization problems. Based on a relative approximation scheme targeting fuzzy membership degree, we formulate two notions of "reducibility" in order to compare the computational complexity of two fuzzy problems. These reducibility notions make it possible to locate the most difficult fuzzy problems in Fuzzy-NPA and in Fuzzy-NPAO.Comment: A4, 10pt, 10 pages. This extended abstract already appeared in the Proceedings of the Joint 7th International Conference on Soft Computing and Intelligent Systems (SCIS 2014) and 15th International Symposium on Advanced Intelligent Systems (ISIS 2014), December 3-6, 2014, Institute of Electrical and Electronics Engineers (IEEE), pp. 29-35, 201
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