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

这个项目的目标是设计算法和统计工具，以计算高效的方式从大量数据中建立复杂的概率模型。这项工作的动机是基因组学中当前的一个重要问题，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，但基因组上的表观遗传标记与细胞之间的变异高度相关。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。虽然已经为此目的产生了大量数据，但对能够对这些数据进行操作并提供具有生物意义的解决方案的计算工具的需求很大。因此，这项工作将推进大型复杂数据集分析的最新水平，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，并向社区发布开源软件。具体地说，该项目将专注于谱学习，它最近为学习概率图形模型的参数提供了原则性和计算效率高的方法。虽然谱学习方法对于一些简单的潜变量模型是已知的，但在现实世界的应用中实现谱学习潜力的一个主要障碍是缺乏相关的统计工具，例如以原则性的方式将这些方法与端到端应用框架连接的正则化和假设检验。该项目建议通过将现代谱学习与计量经济学中关于广义矩方法的经典统计文献相结合来开发这样的统计工具。该项目提出了在谱学习的背景下将复杂图形模型的统计广义矩过程方法表述为约束优化问题，并提出了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数据集建模，以产生能够对大量数据进行操作并提供具有生物学意义的解决方案的方法。这些算法和软件有可能对癌症和精神障碍等复杂人类疾病的理解产生广泛影响。这将为设计针对这些疾病的治疗方法提供基础，并推动社会走向个性化医学的未来。

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.