In this paper, we introduce a novel family of iterative algorithms which carry out $\alpha$-divergence minimisation in a Variational Inference context. They do so by ensuring a systematic decrease at each step in the $\alpha$-divergence between the variational and the posterior distributions. In its most general form, the variational distribution is a mixture model and our framework allows us to simultaneously optimise the weights and components parameters of this mixture model. Our approach permits us to build on various methods previously proposed for $\alpha$-divergence minimisation such as Gradient or Power Descent schemes and we also shed a new light on an integrated Expectation Maximization algorithm. Lastly, we provide empirical evidence that our methodology yields improved results on several multimodal target distributions and on a real data example.

翻译：在本文中，我们提出了一类新颖的迭代算法，用于在变分推断框架中实现α散度最小化。这些算法确保每一步中变分分布与后验分布之间的α散度系统性递减。在其最一般的形式下，变分分布为混合模型，我们的框架能够同时优化该混合模型的权重和分量参数。我们的方法允许我们基于先前提出的多种α散度最小化方法（如梯度下降或幂下降方案）进行构建，同时为集成期望最大化算法提供了新的视角。最后，我们通过实验证明，该方法在多个多峰目标分布以及一个真实数据示例上均取得了更优的结果。