RI: Small: Collaborative Research: New Directions in Spectral Learning with Applications to Comparative Epigenomics

该项目的目标是设计算法和统计工具，以高效的计算方式从大量数据中构建复杂的概率模型。这项工作的动机是基因组学中一个重要的当前问题，即比较表观遗传学。虽然生物体中的每个细胞都有相同的DNA序列，但已知基因组上的表观遗传标记与细胞之间的差异高度相关。生物学中的一个紧迫问题是比较不同细胞类型的表观遗传标记，以了解这些差异。虽然为此目的产生了大量数据，但非常需要能够对这些数据进行操作并提供具有生物学意义的解决方案的计算工具。因此，这项工作将推动大型复杂数据集分析的最新技术，并推动表观基因组学领域的发展。这项工作的更广泛影响包括在机器学习和生物信息学场所组织研讨会和教程，让本科生参与研究，并为社区发布开源软件。具体来说，该项目将专注于谱学习，它最近为概率图模型的参数学习提供了原则性和计算效率高的方法。虽然频谱学习方法以一些简单的潜在变量模型而闻名，但在实际应用中实现频谱学习潜力的主要障碍是缺乏相关的统计工具，如正则化和假设检验，这些工具以原则性的方式将这些方法连接到端到端应用程序框架。本项目拟将现代谱学习与计量经济学中关于广义矩法的经典统计文献相结合，开发这样的统计工具。本项目提出将谱学习背景下复杂图形模型矩过程的统计广义方法作为约束优化问题，并提出解决这些问题的方法。最后，开发的新算法将直接应用于ENCODE和路线图表观基因组学项目的表观基因组学数据集模型，以产生可以在大量数据上操作的方法，并提供具有生物学意义的解决方案。这些算法和软件有可能对理解复杂的人类疾病（如癌症和精神障碍）产生广泛的影响。这将为设计这些疾病的治疗方法提供基础，并推动社会走向个性化医疗的未来。

The goal of this project is to design algorithms and statistical tools to build complex probabilistic models from massive quantities of data in a computationally efficient manner. This work is motivated by an important current problem in genomics, namely comparative epigenetics. While every cell in an organism has the same DNA sequence, epigenetic marks on the genome are known to be highly correlated with variation between cells. A pressing question in biology is to compare the epigenetic marks across different cell types to understand these differences. While massive amounts of data has been generated for this purpose, there is a great need for computational tools that can operate on this data and provide biologically meaningful solutions. This work will thus advance the state-of-the-art in the analysis of large complex data sets and advance the field of epigenomics. The broader impact of the work includes organizing workshops and tutorials at machine learning and bioinformatics venues, involving undergraduate students in research, and releasing open source software for the community.Specifically, this project will focus on spectral learning, which has recently provided principled and computationally efficient methods for learning parameters of probabilistic graphical models. While spectral learning methods are known for some simple latent variable models, a major barrier to realizing the potential of spectral learning in real-world applications is the lack of associated statistical tools such as regularization and hypothesis testing that connect these methods in a principled manner to end-to-end application frameworks. This project proposes to develop such statistical tools by integrating modern spectral learning with the classical statistical literature in econometrics on Generalized Method of Moments. The project proposes to formulate the statistical generalized method of moment procedures for complex graphical models in the context of spectral learning as constrained optimization problems and proposes ways of solving these problems. Finally, the novel algorithms developed will be directly applied to model epigenomics data sets from the ENCODE and Roadmap Epigenomics Projects to yield methods that can operate on the massive quantities of data and provide biologically meaningful solutions. These algorithms and software have the potential to have a widespread impact on the understanding of complex human diseases such as cancer and mental disorders. This will provide a basis for designing therapeutics for these diseases and advance society towards a future of Personalized Medicine.