具有对称信息发散的概率链模型
Probability Link Models with Symmetric Information Divergence
摘要：
本文引入了将一个概率分布转换为另一个的连接函数，使得两个分布之间的Kullback-Leibler和Rényi分歧是对称的。提出了两类通用的链路模型。第一个模型连接了两个生存函数，适用于生存分析和可靠性建模中使用的比例比值和变点等模型。涉及比例优势模型的原型应用程序演示了对称发散措施的优势，非对称措施，用于评估功能的功效和模型平均的目的。其优点包括为模型提供唯一的秩和为模型平均提供唯一的信息权重，其计算量为非对称发散的一半。第二个模型连接两个累积概率分布函数。该模型产生了一个广义的位置模型，它是诸如probit和logit模型的二元概率模型的连续对应物。例如，在生存分析文献中出现的广义probit和logit模型，以及作为与各二进制概率模型对应的生存时间模型的广义Laplace模型和广义Student- $t$模型。最后，生存函数和copula依赖信息的条件之间的对称发散的扩展。
英文摘要：
This paper introduces link functions for transforming one probability distribution to another such that the Kullback-Leibler and Rényi divergences between the two distributions are symmetric. Two general classes of link models are proposed. The first model links two survival functions and is applicable to models such as the proportional odds and change point, which are used in survival analysis and reliability modeling. A prototype application involving the proportional odds model demonstrates advantages of symmetric divergence measures over asymmetric measures for assessing the efficacy of features and for model averaging purposes. The advantages include providing unique ranks for models and unique information weights for model averaging with one-half as much computation requirement of asymmetric divergences. The second model links two cumulative probability distribution functions. This model produces a generalized location model which are continuous counterparts of the binary probability models such as probit and logit models. Examples include the generalized probit and logit models which have appeared in the survival analysis literature, and a generalized Laplace model and a generalized Student-$t$ model, which are survival time models corresponding to the respective binary probability models. Lastly, extensions to symmetric divergence between survival functions and conditions for copula dependence information are presented.
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