Extension and Application of Statistical Models Based on Bregman Divergence

在本研究中，我们重点研究了一类与Bregman散度相关的统计模型，该模型在计算统计量时实现了鲁棒估计。我们提出了这些模型的一些估计方法，并从数据分析应用的角度分析了它们的一些性质。特别地，我们利用正乘法规则的推广推广了统计独立性的定义；扩展是由Bregman散度导出的。我们已经证明，基于广义独立性的统计模型可以减轻传统方法中假设的条件独立性，从而在实际数据分析中成为有用的工具。

In this study, we focused on a class of statistical models associated with the Bregman divergence which achieves robust estimation in calculating statistics. We have proposed some methods for estimation of these models, and analyzed some properties from the viewpoint of application for data analysis. Particularly, we generalized the definition of statistical independence by using an extension of the multiplication rule between positive values; the extension is derived from the Bregman divergence. We have shown that the proposed statistical models based on generalized independence can be useful tools in practical data analysis by alleviating the conditional independence assumed in the conventional methods.