CURVATURE, CONCENTRATION AND ERROR ESTIMATES FOR MARKOV CHAIN MONTE CARLO
CURVATURE, CONCENTRATION AND ERROR ESTIMATES FOR MARKOV CHAIN MONTE CARLO
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DOI：
10.1214/10-aop541
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发表时间：
2009-04
影响因子：
2.3
通讯作者：
A. Joulin;Y. Ollivier
中科院分区：
文献类型：
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作者：
A. Joulin;Y. Ollivier
我们提供了显式的非渐近估计的马尔可夫链的经验平均值的收敛速度，连同高斯或指数控制的经验平均值的偏差。这些估计下举行的“正曲率”的假设表示一种度量遍历性，推广的Ricci曲率从微分几何和有限图，相当于压缩下的路径耦合。
We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a "positive curvature" assumption expressing a kind of metric ergodicity, which generalizes the Ricci curvature from differential geometry and, on finite graphs, amounts to contraction under path coupling.