Convergence and Efficiency of Adaptive Importance Sampling Techniques with Partial Biasing
Convergence and Efficiency of Adaptive Importance Sampling Techniques with Partial Biasing
复制标题
具有部分偏差的自适应重要性采样技术的收敛性和效率
DOI：
10.1007/s10955-018-1992-2
复制
发表时间：
2016
影响因子：
1.6
通讯作者：
G. Stoltz
中科院分区：
文献类型：
--
作者：
G. Fort;B. Jourdain;T. Lelièvre;G. Stoltz
我们提出了一种新的Monte Carlo方法来有效地采样多峰分布（已知的归一化常数）。我们考虑离散时间自愈伞采样方法的推广，这也可以被看作是一个推广的好脾气的元自适应。动态是基于自适应的重要性技术。重要性函数依赖于形成空间分区的不相交集合的权重（即相对概率）。这些权重是未知的，但在飞行中学习，产生自适应算法。在计算统计物理学的背景下，这些权重的对数是自由能，直到一个加性常数，定义分区的离散值函数被称为集体变量。该算法福尔斯属于Wang-Landau类型方法的一般类，并且是原始自修复伞采样方法在两个方面的推广：（i）更新策略导致已经访问的集合的更大惩罚强度，以便更快地从亚稳态逃逸，以及（ii）仅使用自由能的一小部分来使目标分布偏置，以增加有效样本容量和减小重要抽样估计量的方差。我们证明了算法的收敛性，并通过一个玩具例子数值分析了其效率。
We propose a new Monte Carlo method to efficiently sample a multimodal distribution (known up to a normalization constant). We consider a generalization of the discrete-time Self Healing Umbrella Sampling method, which can also be seen as a generalization of well-tempered metadynamics. The dynamics is based on an adaptive importance technique. The importance function relies on the weights (namely the relative probabilities) of disjoint sets which form a partition of the space. These weights are unknown but are learnt on the fly yielding an adaptive algorithm. In the context of computational statistical physics, the logarithm of these weights is, up to an additive constant, the free-energy, and the discrete valued function defining the partition is called the collective variable. The algorithm falls into the general class of Wang–Landau type methods, and is a generalization of the original Self Healing Umbrella Sampling method in two ways: (i) the updating strategy leads to a larger penalization strength of already visited sets in order to escape more quickly from metastable states, and (ii) the target distribution is biased using only a fraction of the free-energy, in order to increase the effective sample size and reduce the variance of importance sampling estimators. We prove the convergence of the algorithm and analyze numerically its efficiency on a toy example.