Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization

Dukkipati, Ambedkar; Murty, M. Narasimha; Bhatnagar, Shalabh

doi:10.1016/j.physa.2005.06.072

Cited by 24 publications

(19 citation statements)

References 28 publications

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“…Secondly, the KL-divergence plays a central role in the Principle of minimum of relative Boltzmann-Gibbs entropy, MinxEnt. According to known results (see, e.g., Borland et al, 1998, Dukkipati et al, 2006, Tsallis 2008, etc. ), the distribution m ( x ) that provides minimum for I KL [ m : r ] given the mean value of m equal to s , is the Boltzmann distribution…”

Section: Dynamical Principles Of Minimum Of Shannon Information Lossmentioning

confidence: 90%

Mathematical Modeling of Extinction of Inhomogeneous Populations

Karev

Kareva

2016

Bull Math Biol

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Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception.

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Section: Dynamical Principles Of Minimum Of Shannon Information Lossmentioning

confidence: 90%

Mathematical Modeling of Extinction of Inhomogeneous Populations

Karev

Kareva

2016

Bull Math Biol

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“…For this we will use an analogue of Pythagoras' theorem for relative entropies as first derived by Csiszar [9]. It has also been called the triangle equality by others [10]:…”

Section: Combining the Different Concepts In One Equationmentioning

confidence: 99%

Modeling the world by minimizing relative entropy

Ven¹

2012

AIP Conference Proceedings

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Relative entropy and the principle of minimum relative entropy are proposed as fundamental concepts that can be used as a foundation for designing and building adaptive, generally intelligent agents that build a model of the world. An equation is derived that describes how such an agent can build a model of the world by minimizing relative entropies. With this equation we prove that the agent then continually improves its model of the world. A main advantage of this equation and the derivation is that it clarifies and shows the relation between different uses and interpretations of relative entropy, such as measures of dissimilarity, learning progress or surprise, minimization and maximization of relative entropies for minimal belief updates and how it can select actions that lead to exploratory and curious behavior. As an example we applied our equation and approach to play the game of Mastermind.

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“…Specifying q = 2 − q * in the numerator of (38) and evoking (4), yields the canonical transition probability…”

Section: Case Formentioning

confidence: 99%

“…• A-priori specifying the nonextensivity parameter q and the effective nonextensive trade-off parameter for a single source alphabet β * (x) obtained from (38) for all source alphabets, the expected distortion D =< d(x,x) > p(x,x) is obtained. Choosing a random data point inX (the convex set of probability distributions B, described in Sections 4.1 and 4.2), an initial guess for p(x) is made.…”

Section: Nonextensive Alternating Minimization Algorithm Revisitedmentioning

confidence: 99%

Generalized statistics framework for rate distortion theory

Venkatesan

Plastino

2009

Physica A: Statistical Mechanics and its Applications

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Variational principles for the rate distortion (RD) theory in lossy compression are formulated within the ambit of the generalized nonextensive statistics of Tsallis, for values of the nonextensivity parameter satisfying 0 < q < 1 and q > 1. Alternating minimization numerical schemes to evaluate the nonextensive RD function, are derived. Numerical simulations demonstrate the efficacy of generalized statistics RD models.

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Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization

Cited by 24 publications

References 28 publications

Mathematical Modeling of Extinction of Inhomogeneous Populations

Mathematical Modeling of Extinction of Inhomogeneous Populations

Modeling the world by minimizing relative entropy

Generalized statistics framework for rate distortion theory

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