Evolutionary and energy-domain Monte Carlo algorithms and their applications

摘要为DMS -0505732 PI：教授Wing Hung Wong机构：斯坦福大学标题：进化和能量域蒙特卡罗算法及其应用本项目将开发两个新的蒙特卡罗模拟算法，并将其应用于科学和技术中的几个问题。第一种方法，称为进化蒙特卡罗，是由PI的实验室在先前的NSF支持下引入的。它已被应用于具有挑战性的问题，如HP模型在蛋白质折叠和CP为基础的模型选择的优秀成果。在这里，它提出了进化MC被开发的有向无环图模型（DAG）的网络结构的计算推理。 第二种方法，称为等能量采样，正处于PI及其合作者开发的早期阶段。我们的想法是从等能量环中产生样本，每个环的能量都在一个有限的值区间内。利用能量-温度对偶性，允许从微正则平均值（即等能量环内的平均值）的估计来估计玻尔兹曼平均值（即对应于固定温度的平均值）。除了给出玻尔兹曼平均值的估计外，这种方法还提供了“态密度”函数和配分函数的估计。因此，等能量采样可以在一次运行中提供所有热力学量的信息，因此它应该是一个非常有吸引力的算法在物理应用中，如蛋白质折叠。马尔可夫链蒙特卡罗方法的最新发展使得统计建模和推断的应用越来越广泛。对于许多重要的应用，如DNA模体采样，蛋白质折叠，因果网络结构的统计推断，蒙特卡罗计算已成为一个不可或缺的工具。在这个项目中提出的工作将导致显着提高性能的蒙特卡罗算法在复杂的能量景观的问题，因此将使它可行的应用这种方法更广泛的问题。

Abstract for DMS - 0505732PI: Professor Wing Hung WongINSTITUTION: STANFORD UNIVERSITYTITLE: Evolution and Energy Domain Monte Carlo algorithms and their applicationsThis project will develop two new algorithms for Monte Carlo simulation and applied them to several problems in science and technology. The first method, called Evolutionary Monte Carlo, was introduced by the PI's laboratory under prior NSF support. It has been applied with excellent results in challenging problems such as the HP model in protein folding and Cp-based model selection. Here, it is proposed that Evolutionary MC be developed for the computational inference of network structure for directed acylic graphical models (DAG). The second method, called equi-energy sampling, is in an early stage of development by the PI and his collaborators. The idea is to generate samples from the equi-energy rings each of them having the energy lying within a restricted interval of values. An energy-temperature duality is exploited to allow the estimation of a Boltzmann average (i.e. averages corresponding to a fixed temperature) from estimates of the micro-canonical averages (i.e. averages within equi-energy rings). In addition to giving estimates of Boltzmann averages, this approach also provide estimates for the "density of states" function and the partition function. Thus equi-energy sampling can provide information for all thermodynamic quantities in a single run, and for this reason it should be a very attractive algorithm in physical applications such as protein folding. Recent development of Markov Chain Monte Carlo methods has allowed the application of statistical modeling and inference to more and more application areas. For many important applications such as DNA motif sampling, protein folding, and statistical inference of causal network structures, Monte Carlo computation has become an indispensable tool. The work proposed in this project will result in significant improvement of the performance Monte Carlo algorithms in problems with complex energy landscapes, and therefore will make it feasible to apply this method to a wider spectrum of problems.