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首页> 外文期刊>Information Theory, IEEE Transactions on >f -Divergence Inequalities
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f -Divergence Inequalities

机译：f-散度不等式

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摘要

This paper develops systematic approaches to obtain f -divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on finding the best possible constant upper bounding a ratio of f -divergences. Another approach used for the derivation of bounds among f -divergences relies on moment inequalities and the logarithmic-convexity property, which results in tight bounds on the relative entropy and Bhattacharyya distance in terms of χ2 divergences. A rich variety of bounds are shown to hold under boundedness assumptions on the relative information. Special attention is devoted to the total variation distance and its relation to the relative information and relative entropy, including “reverse Pinsker inequalities,” as well as on the Eγ divergence, which generalizes the total variation distance. Pinsker's inequality is extended for this type of f -divergence, a result which leads to an inequality linking the relative entropy and relative information spectrum. Integral expressions of the Rényi divergence in terms of the relative information spectrum are derived, leading to bounds on the Rényi divergence in terms of either the variational distance or relative entropy.
机译：本文开发了系统的方法来获得f散度不等式，处理了在任意字母上定义的几对概率测度。功能支配是一种这样的方法，其中特别着重于找到最佳的恒定上边界，该上边界的比率为f-散度。用于推导f散度之间界限的另一种方法依赖于矩不等式和对数凸性质，这导致相对熵和Bhattacharyya距离在χ2散度方面具有严格的界限。在相对信息的有界假设下，显示了各种各样的界。特别注意总变化距离及其与相对信息和相对熵的关系，包括“反向Pinsker不等式”，以及Eγ散度，它概括了总变化距离。这种类型的f-散度扩展了Pinsker不等式，其结果导致了将相对熵和相对信息谱联系起来的不等式。根据相对信息谱推导了雷尼散度的积分表达式，从而导致了雷尼散度的变分距离或相对熵范围。

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