This paper introduces the $f$-EI$(\phi)$ algorithm, a novel iterative algorithm which operates on measures and performs $f$-divergence minimisation in a Bayesian framework. We prove that for a rich family of values of $(f,\phi)$ this algorithm leads at each step to a systematic decrease in the $f$-divergence and show that we achieve an optimum. In the particular case where we consider a weighted sum of Dirac measures and the $\alpha$-divergence, we obtain that the calculations involved in the $f$-EI$(\phi)$ algorithm simplify to gradient-based computations. Empirical results support the claim that the $f$-EI$(\phi)$ algorithm serves as a powerful tool to assist Variational methods.

翻译：本文介绍了美元-欧元(\phi)的算法,这是一种新型的迭代算法,在贝叶斯框架范围内以计量方式运作并进行美元-美元-美元(phi)的最小化。我们证明,对于一个价值为(f,\phi)美元的富裕家庭,这种算法每一步都会导致美元-美元(f,\phi)值的系统性下降,并表明我们取得了最佳效果。在特定情况下,我们认为Dirac措施的加权总和和和$/alpha美元/divence,我们得到的是,将美元-美元(hipe)的算法简化为基于梯度的计算所涉及的计算。 经验性结果支持了一项主张,即美元-美元(hipi)的算法是协助改变方法的有力工具。