论文标题
在多模式目标分布上的顺序蒙特卡洛估计器的有限样品复杂性
Finite Sample Complexity of Sequential Monte Carlo Estimators on Multimodal Target Distributions
论文作者
论文摘要
我们证明了顺序蒙特卡洛（SMC）算法的有限样品复杂度，该算法仅需要相关的马尔可夫核的局部混合时间。当目标分布是多模式的，而马尔可夫内核的全局混合速度很慢时，我们的边界特别有用。在这种情况下，我们的方法确定了SMC比相应的Markov链Monte Carlo（MCMC）估计量的好处。缺乏全局混合是通过依次控制SMC重新采样程序引入的偏差来解决的。我们将这些结果应用于对数凸出分布的混合物下的近似期望获得复杂性界限，并表明SMC为某些困难的多模式问题提供了完全多项式时间随机近似方案，而相应的Markov链采样器的指数缓慢。最后，我们比较了通过在相同问题上使用我们对钢结战的马尔可夫链的现有界限获得的界限。
We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated Markov kernels. Our bounds are particularly useful when the target distribution is multimodal and global mixing of the Markov kernel is slow; in such cases our approach establishes the benefits of SMC over the corresponding Markov chain Monte Carlo (MCMC) estimator. The lack of global mixing is addressed by sequentially controlling the bias introduced by SMC resampling procedures. We apply these results to obtain complexity bounds for approximating expectations under mixtures of log-concave distributions and show that SMC provides a fully polynomial time randomized approximation scheme for some difficult multimodal problems where the corresponding Markov chain sampler is exponentially slow. Finally, we compare the bounds obtained by our approach to existing bounds for tempered Markov chains on the same problems.
