论文标题
汉密尔顿蒙特卡洛骗子
Hamiltonian Monte Carlo Swindles
论文作者
论文摘要
汉密尔顿蒙特卡洛（HMC）是一种强大的马尔可夫链蒙特卡洛（MCMC）算法，用于估计对连续非归一化概率分布的期望。 MCMC估计量通常比具有I.I.D.的经典蒙特卡洛具有更高的方差。由于自相关引起的样本；大多数MCMC研究试图减少这些自相关。在这项工作中，我们探索了一种基于两个经典的蒙特卡洛“ swindles”的互补方法减少：首先，运行一个辅助耦合链，靶向目标分布的可拖动近似值，并以辅助样本为控制变化；其次，通过运行两个具有翻转随机性的链来产生抗相关（“反心”）样品。以前在Gibbs采样器和随机步行都会算法的背景下探索了这两种想法，但我们认为，根据HMC理论文献的最新耦合结果，它们已经成熟地适应HMC。对于许多后验分布，我们发现这些损失产生的样本量比普通的HMC大，并且比大都市调整后的兰格文算法和随机步行大都市比类似的swindles更有效。
Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) algorithm for estimating expectations with respect to continuous un-normalized probability distributions. MCMC estimators typically have higher variance than classical Monte Carlo with i.i.d. samples due to autocorrelations; most MCMC research tries to reduce these autocorrelations. In this work, we explore a complementary approach to variance reduction based on two classical Monte Carlo "swindles": first, running an auxiliary coupled chain targeting a tractable approximation to the target distribution, and using the auxiliary samples as control variates; and second, generating anti-correlated ("antithetic") samples by running two chains with flipped randomness. Both ideas have been explored previously in the context of Gibbs samplers and random-walk Metropolis algorithms, but we argue that they are ripe for adaptation to HMC in light of recent coupling results from the HMC theory literature. For many posterior distributions, we find that these swindles generate effective sample sizes orders of magnitude larger than plain HMC, as well as being more efficient than analogous swindles for Metropolis-adjusted Langevin algorithm and random-walk Metropolis.
