Tsallis FPD generalizes standard fully probabilistic design using Tsallis divergence and proves that a double backwards induction fixed-point iteration converges to an optimal solution.
On R´ enyi and Tsallis entropies and divergences for exponential families
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abstract
Many common probability distributions in statistics like the Gaussian, multinomial, Beta or Gamma distributions can be studied under the unified framework of exponential families. In this paper, we prove that both R\'enyi and Tsallis divergences of distributions belonging to the same exponential family admit a generic closed form expression. Furthermore, we show that R\'enyi and Tsallis entropies can also be calculated in closed-form for sub-families including the Gaussian or exponential distributions, among others.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
An entropy-corrected action principle on superspace recovers the Wheeler-DeWitt equation for gravity and a Schrödinger equation for coupled scalar fields with emergent time and a G ħ² correction term.
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Towards Tsallis Fully Probabilistic Design
Tsallis FPD generalizes standard fully probabilistic design using Tsallis divergence and proves that a double backwards induction fixed-point iteration converges to an optimal solution.
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Quantizing gravitational fields with an entropy-corrected action principle
An entropy-corrected action principle on superspace recovers the Wheeler-DeWitt equation for gravity and a Schrödinger equation for coupled scalar fields with emergent time and a G ħ² correction term.