This paper introduces a variational approximation framework using direct optimization of what is known as the {\it scale invariant Alpha-Beta divergence} (sAB divergence). This new objective encompasses most variational objectives that use the Kullback-Leibler, the R{\'e}nyi or the gamma divergences. It also gives access to objective functions never exploited before in the context of variational inference. This is achieved via two easy to interpret control parameters, which allow for a smooth interpolation over the divergence space while trading-off properties such as mass-covering of a target distribution and robustness to outliers in the data. Furthermore, the sAB variational objective can be optimized directly by repurposing existing methods for Monte Carlo computation of complex variational objectives, leading to estimates of the divergence instead of variational lower bounds. We show the advantages of this objective on Bayesian models for regression problems.

本文介绍了一种使用直接优化“尺度不变的Alpha-Beta离散度”（sAB离散度）的变分逼近框架，该新目标包含了大多数使用Kullback-Leibler、Rényi或gamma离散度的变分目标，还提供了以前在变分推理环境中从未利用过的目标函数。这通过两个易于解释的控制参数实现，可以在离散度空间上平滑地插值，同时交换目标分布的质量覆盖和数据异常值鲁棒性等属性。此外，通过重新定位用于复杂变分目标的蒙特卡罗计算现有方法，可以直接优化sAB变分目标，导致离散度的估计值而不是变分下限。我们展示了这个目标在回归问题的贝叶斯模型上的优势。

可变推断中的Alpha-Beta散度