论文标题
马尔可夫评分攀登：用KL的变异推断（P || Q）
Markovian Score Climbing: Variational Inference with KL(p||q)
论文作者
论文摘要
现代变异推理（VI）使用随机梯度来避免棘手的期望，从而在复杂模型中实现了大规模的概率推断。 VI提出了一个近似分布Q的家族，然后找到该家族的成员最接近确切的后p。传统上，VI算法通常为计算便利性而最大程度地减少“独家Kullback-Leibler（kl）” KL（Q || P）。然而，最近的研究还集中在“包容性的KL” KL（P || Q）上，该研究具有良好的统计属性，使其更适合某些推理问题。本文开发了一种简单的算法，用于可靠地使用具有消失的偏差的随机梯度可靠地最大程度地减少包容性KL。我们称之为马尔可夫评分攀登（MSC）的方法将其收敛到包含KL的局部最佳。它不会遭受现有方法固有的系统错误，例如重新恢复的唤醒和神经适应性顺序蒙特卡洛，这导致了最终估计的偏见。我们说明了玩具模型上的融合，并演示了MSC在分类的贝叶斯概率回归以及财务数据的随机波动模型上的实用性。
Modern variational inference (VI) uses stochastic gradients to avoid intractable expectations, enabling large-scale probabilistic inference in complex models. VI posits a family of approximating distributions q and then finds the member of that family that is closest to the exact posterior p. Traditionally, VI algorithms minimize the "exclusive Kullback-Leibler (KL)" KL(q || p), often for computational convenience. Recent research, however, has also focused on the "inclusive KL" KL(p || q), which has good statistical properties that makes it more appropriate for certain inference problems. This paper develops a simple algorithm for reliably minimizing the inclusive KL using stochastic gradients with vanishing bias. This method, which we call Markovian score climbing (MSC), converges to a local optimum of the inclusive KL. It does not suffer from the systematic errors inherent in existing methods, such as Reweighted Wake-Sleep and Neural Adaptive Sequential Monte Carlo, which lead to bias in their final estimates. We illustrate convergence on a toy model and demonstrate the utility of MSC on Bayesian probit regression for classification as well as a stochastic volatility model for financial data.
