论文标题
加速随机概率推断
Accelerating Stochastic Probabilistic Inference
论文作者
论文摘要
最近，由于其能够找到概率模型的良好后近似值，随机变异推理（SVI）越来越有吸引力。根据自然梯度的嘈杂估计，它通过随机优化优化了变异目标。但是，几乎所有最先进的SVI算法都是基于一阶优化算法，并且通常患有不良的收敛速率。在本文中，我们通过提出一种基于二阶的随机变异推理方法来弥合二阶方法和随机变异推理之间的差距。特别是，首先，我们得出了变异目标的Hessian矩阵。然后，我们设计了两个数值方案，以有效地实现二阶SVI。对合成数据集和实际数据集进行了彻底的经验评估，以备份所提出方法的有效性和效率。
Recently, Stochastic Variational Inference (SVI) has been increasingly attractive thanks to its ability to find good posterior approximations of probabilistic models. It optimizes the variational objective with stochastic optimization, following noisy estimates of the natural gradient. However, almost all the state-of-the-art SVI algorithms are based on first-order optimization algorithm and often suffer from poor convergence rate. In this paper, we bridge the gap between second-order methods and stochastic variational inference by proposing a second-order based stochastic variational inference approach. In particular, firstly we derive the Hessian matrix of the variational objective. Then we devise two numerical schemes to implement second-order SVI efficiently. Thorough empirical evaluations are investigated on both synthetic and real dataset to backup both the effectiveness and efficiency of the proposed approach.
