将无限交换的并行温标引入跳跃粒子采样，加速多峰分布收敛。
Bouncy particle sampler with infinite exchanging parallel tempering
- 用无限交换率并行温标提升跳跃粒子采样效率
- 在多峰分布上显著加快收敛速度
- 适合需要快速采样的复杂后验推断任务
贝叶斯推断有助于获得泛化误差小的预测分布。由于后验分布通常无法解析计算，常采用变分贝叶斯推断或采样方法近似。对连续变量部分常用哈密顿蒙特卡洛（HMC），离散变量部分则用马尔可夫链蒙特卡洛（MCMC）。另一种采样方法——跳跃粒子采样（BPS）结合匀速运动与随机反射实现采样，相比HMC更易设置模拟参数。为加速收敛，本文将并行温标（PT）引入BPS，提出逆温度交换率为无穷大时的算法。数值模拟表明该方法在多峰分布上具有有效性。
原文摘要 · Abstract (English)
Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to approximate posterior distributions. When we obtain samples from a posterior distribution, Hamiltonian Monte Carlo (HMC) has been widely used for the continuous variable part and Markov chain Monte Carlo (MCMC) for the discrete variable part. Another sampling method, the bouncy particle sampler (BPS), has been proposed, which combines uniform linear motion and stochastic reflection to perform sampling. BPS was reported to have the advantage of being easier to set simulation parameters than HMC. To accelerate the convergence to a posterior distribution, we introduced parallel tempering (PT) to BPS, and then proposed an algorithm when the inverse temperature exchange rate is set to infinity. We performed numerical simulations and demonstrated its effectiveness for multimodal distribution.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。