Game theory, maximum entropy, minimum discrepancy and robust Bayesian decision theory

Game Theory, Maximum Entropy, Minimum Discrepancy and Robust Bayesian Decision Theory

We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium theory of zero-sum games between Decision Maker and Nature, these two problems are shown to be dual to each other, the solution to each providing that to the...

Game Theory , Maximum Generalized Entropy , Minimum Dis repan y , Robust Bayes

The Maximum Entropy Method Of Moments And Bayesian Probability Theory

The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) ...

Decision Theory III - Game Theory

We briefly introduce and discuss two two-player non-zero-sum games, mainly to illustrate that such games are substantially more complex to investigate than zero-sum games. Actually, the key aspect of such games is that the sum of the pay-offs to the two players is not constant over all pairs of strategies, as constant sum games are equivalent to zero-sum games (think about this; one can imagine...

Maximum Entropy and Learning Theory

We derive the learning theory recently reported by Tishby, Levin, and Solla (TLS) without statistical mechanics. We show that the theory generally applies to any problem of modeling data. We analyze an elementary example for which we find the predictions consistent with intuition and conventional statistical results. We numerically examine the more realistic problem of training a competitive ne...