Topic

# Minimax

About: Minimax is a research topic. Over the lifetime, 10372 publications have been published within this topic receiving 271034 citations. 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,.

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08 Dec 2014TL;DR: A new framework for estimating generative models via an adversarial process, in which two models are simultaneously train: 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.

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.

38,211 citations

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01 Jan 1959

TL;DR: The general decision problem, the Probability Background, Uniformly Most Powerful Tests, Unbiasedness, Theory and First Applications, and UNbiasedness: Applications to Normal Distributions, Invariance, Linear Hypotheses as discussed by the authors.

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.

6,480 citations

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22 Dec 2012

TL;DR: An overview of statistical decision theory, which emphasizes the use and application of the philosophical ideas and mathematical structure of decision theory.

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.

5,573 citations

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20 Dec 2004

TL;DR: This chapter discusses Monte Carol methods, the least-absolute values criterion and the minimax criterion, and their applications to functional inverse problems.

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

5,249 citations

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01 Jul 1986TL;DR: The mountain pass theorem and its application in Hamiltonian systems can be found in this paper, where the saddle point theorem is extended to the case of symmetric functionals with symmetries and index theorems.

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.

3,685 citations