论文标题
连续脾气暴躁的PDMP采样器
Continuously-Tempered PDMP Samplers
论文作者
论文摘要
新的采样算法基于模拟连续时间随机过程，称为零件确定性马尔可夫过程（PDMP）表现出了相当大的希望。但是，这些方法可能难以从多模式或重尾分布中取样。我们展示了在这种情况下，调速想法如何改善PDMP的混合。 We introduce an extended distribution defined over the state of the posterior distribution and an inverse temperature, which interpolates between a tractable distribution when the inverse temperature is 0 and the posterior when the inverse temperature is 1. The marginal distribution of the inverse temperature is a mixture of a continuous distribution on [0,1) and a point mass at 1: which means that we obtain samples when the inverse temperature is 1, and these are draws from the posterior, but sampling算法还将在较低温度下探索分布，以改善混合。我们展示了如何实现PDMP，尤其是Zig-Zag采样器，以从这样的扩展分布中进行采样。所得的算法易于实现，我们从经验上表明，它可以在挑战多模式后代的基于PDMP的现有采样器上胜过。
New sampling algorithms based on simulating continuous-time stochastic processes called piece-wise deterministic Markov processes (PDMPs) have shown considerable promise. However, these methods can struggle to sample from multi-modal or heavy-tailed distributions. We show how tempering ideas can improve the mixing of PDMPs in such cases. We introduce an extended distribution defined over the state of the posterior distribution and an inverse temperature, which interpolates between a tractable distribution when the inverse temperature is 0 and the posterior when the inverse temperature is 1. The marginal distribution of the inverse temperature is a mixture of a continuous distribution on [0,1) and a point mass at 1: which means that we obtain samples when the inverse temperature is 1, and these are draws from the posterior, but sampling algorithms will also explore distributions at lower temperatures which will improve mixing. We show how PDMPs, and particularly the Zig-Zag sampler, can be implemented to sample from such an extended distribution. The resulting algorithm is easy to implement and we show empirically that it can outperform existing PDMP-based samplers on challenging multimodal posteriors.
