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Maximum Entropy method with non-linear moment constraints: challenges
| Content Provider | CiteSeerX |
|---|---|
| Author | Grendar, M. |
| Abstract | Abstract. Traditionally, the Method of (Shannon-Kullback’s) Relative Entropy Maximization (REM) is considered with linear moment constraints. Here, the method is studied with frequency moment constraints which are non-linear in probabilities. The constraints challenge some justifications of REM: a) Probabilistic justification of REM via Conditioned Weak Law of Large Numbers cannot be invoked since the feasible set of distributions which is defined by frequency moment constraints admits several entropy maximizing distributions (I-projections), b) Axiomatic justifications of REM are developed for linear moment constraints/convex sets. However, REM is not left completely unjustified in this setting, since Entropy Concentration Theorem and Maximum Probability Theorem can be applied. Maximum Rényi/Tsallis ’ entropy method (maxTent) is as well considered here due to nonlinearity of X-frequency moment constraints which are used in Non-extensive Thermodynamics. It is shown that under X-frequency moment constraints maxTent distribution can be unique and different than the I-projection. This implies that maxTent does not choose the most probable distribution and that the maxTent distribution is asymptotically conditionally improbable. Thus, what are adherents of maxTent accomplishing when they maximize Rényi’s or Tsallis ’ entropy? 1 |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Non-linear Moment Constraint Maximum Entropy Method Frequency Moment Constraint Several Entropy X-frequency Moment Constraint Maxtent Distribution Conditioned Weak Law Maximum Nyi Tsallis Entropy Method X-frequency Moment Constraint Axiomatic Justification Probabilistic Justification Relative Entropy Maximization Non-extensive Thermodynamics Linear Moment Constraint Linear Moment Constraint Convex Set Entropy Concentration Theorem Maximum Probability Theorem Maxtent Distribution Feasible Set Probable Distribution Large Number Cannot Tsallis Entropy |
| Content Type | Text |
| Resource Type | Article |
