197,125 research outputs found
The Complexity of Optimizing over a Simplex, Hypercube or Sphere: A Short Survey
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
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
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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