Computational Inference, Monte Carlo, and Scientific Applications

题目：计算推理、蒙特卡罗方法和科学应用随着自动化、高通量实验协议和数据收集技术的出现，许多科学技术领域的研究和发现越来越受到数据驱动和计算密集型的影响。本课题研究的应用领域包括分子生物学、生物技术和神经科学。这些领域实验数据的快速积累已经超出了科学家的分析能力，需要先进的统计方法来实现分析过程的自动化，并利用这些研究背后复杂的数据结构和广泛的科学知识。计算推理是指依靠密集计算从大规模数据和基于知识的模型中提取信息的统计建模和推理过程。该项目的长期目标是推进计算推理的方法，并将其应用于上述科学领域的几个重要问题的解决。在几乎所有的大规模计算推理过程中，一个关键步骤是通过蒙特卡罗采样研究后验密度（或研究似然函数的相关问题）。成功的抽样可以立即推断出研究者感兴趣的任何参数或预测。因此，这个项目的第一个具体目标是开发蒙特卡罗模拟方法，有效地采样复杂的，多模态分布。这一核心计算问题的进展不仅将促进有效的计算推理，而且还将对其他科学任务如分子结构模拟和组合优化产生兴趣。将研究三种方法：a)进化蒙特卡罗方法，其中结构群体是进化的，个体结构，包括重组结构，在群体中不断竞争生存；b)通过更好的方法处理倾斜的权重分布，进一步发展顺序重要性抽样和动态重要性抽样；c)多层次计算模型。结合上述方法的混合算法也将被研究。其中一些方法将用于研究理解蛋白质构象的能量景观的重大挑战问题。该项目的第二个具体目标是为两个进一步的科学问题开发计算推理工具：i)基于隐马尔可夫模型的DNA和蛋白质序列的多重排列和聚类，以及在人类基因组编码区域分析中的使用；ii)为纹理识别和原始草图等低级视觉任务开发分层计算模型。如果成功，本项目开发的方法将使计算推理得到更广泛的应用，并将对当前科学前沿的三个相当重要的问题作出直接贡献。

Title: Computational inference, Monte Carlo methods, and scientific applicationsWith the advent of automated, high-throughput experimental protocols and data collection techniques, research and discoveries in many areas of science and technology have become increasingly data driven and computation intensive. The applications motivating the research in this project arise from molecular biology, biotechnology and neural science. The rapid accumaulation of experimental data in these areas have outstriped scientists' ability to analyze them, and advanced statistical methods are needed to automate the analysis process and to exploit the complex data structure and extensive scientific knowledge underlying such studies. Computational inference refers to statistical modeling and inference procedures that rely on intensive computation to extract information from large scale data and knowledge-based models. The board, long term goal of this project is to advance the methodologies of computational inference and apply them towards the solution of several important problems in the aforementioned scientific areas. A critical step in almost all large scale computational inference procedure is the study of the posterior density through Monte Carlo sampling (or the related problem of studying the likelihood function). Successful sampling leads immediately to the inference of any parameter or prediction of interest to the investigator. Thus the first specific goal of this project is to develop Monte Carlo simulation methods that are effective in sampling complex, multimodal distributions. Advances in this core computational problem will not only facilitate effective computational inference, but will also be of interest to other scientific tasks such as simulation of molecular structures and combinatorial optimization. Three approaches will be investigated: a) an evolutionary Monte Carlo approach where a population of structures are evolved and individual structures, including recombinant ones, are continuously competing for survival in the population, b) further development of sequential importance sampling and dynamic importance sampling through better methods to handle skewed weight distributions, c) multi-level computational models. Hybrid algorithms combining the above approaches will also be investigated. Some of these methods will be used to investigate the grand-challenge problem of understanding the energy landscape of protein conformation. The second specific goal of this project is the development of computational inference tools for two further scientifc problems: i) multiple alignment and clustering of DNA and protein sequences based on hidden Markov models, and the use of these in the analysis of human genome coding regions, ii) the development of hierarchical computational models for low-level vision task such as texture recognition and primal sketching. If successful, the methods developed in this project will enable the wider application of computational inference and will also result in direct contributions to three problems of considerable importance in the current scientific frontier.