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About: Minimax is a(n) research topic. Over the lifetime, 10372 publication(s) have been published within this topic receiving 271034 citation(s). The topic is also known as: minimax means maximise the minimum gain which is adopted by left hand side player , and maxmin means minimise the maximum loss which is adopted by upper player , both can be used in zero sum game,. more


Open accessJournal ArticleDOI: 10.3156/JSOFT.29.5_177_2
Ian Goodfellow1, Jean Pouget-Abadie1, Mehdi Mirza1, Bing Xu1  +4 moreInstitutions (2)
08 Dec 2014-
Abstract: We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples. more

Topics: Generative model (64%), Discriminative model (54%), Approximate inference (53%) more

29,410 Citations

Open accessBook
01 Jan 1959-
Abstract: The General Decision Problem.- The Probability Background.- Uniformly Most Powerful Tests.- Unbiasedness: Theory and First Applications.- Unbiasedness: Applications to Normal Distributions.- Invariance.- Linear Hypotheses.- The Minimax Principle.- Multiple Testing and Simultaneous Inference.- Conditional Inference.- Basic Large Sample Theory.- Quadratic Mean Differentiable Families.- Large Sample Optimality.- Testing Goodness of Fit.- General Large Sample Methods. more

6,474 Citations

Open accessBook
22 Dec 2012-
Abstract: 1. Basic concepts 2. Utility and loss 3. Prior information and subjective probability 4. Bayesian analysis 5. Minimax analysis 6. Invariance 7. Preposterior and sequential analysis 8. Complete and essentially complete classes Appendices. more

Topics: Robust Bayesian analysis (66%), Bayesian inference (58%), Decision theory (58%) more

5,268 Citations

Open accessBook
20 Dec 2004-
Abstract: 1 The general discrete inverse problem 2 Monte Carol methods 3 The least-squares criterion 4 Least-absolute values criterion and minimax criterion 5 Functional inverse problems 6 Appendices 7 Problems References Index more

Topics: Circle criterion (62%), Inverse problem (58%), Minimax (53%) more

4,634 Citations

Open accessBook
Paul Rabinowitz1Institutions (1)
01 Jul 1986-
Abstract: An overview The mountain pass theorem and some applications Some variants of the mountain pass theorem The saddle point theorem Some generalizations of the mountain pass theorem Applications to Hamiltonian systems Functionals with symmetries and index theorems Multiple critical points of symmetric functionals: problems with constraints Multiple critical points of symmetric functionals: the unconstrained case Pertubations from symmetry Variational methods in bifurcation theory. more

Topics: Mountain pass theorem (72%), Mountain pass (56%), Palais–Smale compactness condition (54%) more

3,434 Citations

No. of papers in the topic in previous years

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Topic's top 5 most impactful authors

T. Tony Cai

62 papers, 3.7K citations

Martin J. Wainwright

43 papers, 3.1K citations

Ian R. Petersen

42 papers, 744 citations

William E. Strawderman

38 papers, 740 citations

Alexandre B. Tsybakov

31 papers, 2.2K citations

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