RI: Small: Finding Patterns in Complex Data with Probablistic Graphical Models

在各种科学、社会和商业应用中，发现模式（变量组一起工作）及其在高维问题中的依赖关系的能力变得至关重要。 重要领域包括癌症基因组学、气候科学、森林生态学、医疗保健和社交媒体分析。典型的模式涉及一组或多组变量，这些变量在某些情况下共同表现出相似或相关的行为。在预测环境中，某些变量组的激活通常用作预测任务的关键信号。迫切需要超越识别成对相互作用的概率模型，以了解变量之间的高阶相互作用。为此，该项目将研究基于结构约束依赖估计和概率图模型中的高维推理的新方法。这项工作将考虑两个重要的应用：气候和家庭护理。在地球仪范围内，气候变化正在影响降水等天气事件的频率和强度。所提出的方法将能够更准确地模拟降水驱动的水文事件。在美国，到2019年，医疗保健支出预计将增加到国内生产总值（GDP）的19.6%。拟议的家庭护理工作范围独特，将广泛适用于任何医疗保健数据，从而为未来有意义地使用电子健康记录奠定基础，这是美国的国家优先事项。该项目自然会产生许多教育机会，并将通过课堂教学和相关模式吸引学生。该项目将让代表性不足的群体参与研究，并通过研讨会和教程传播研究结果。从技术角度来看，高阶交互作用的概率模式分析存在两个核心挑战：组合挑战，因为人们必须潜在地考虑所有可能的变量子集及其相互作用，以及统计挑战，由于通常只有少量的样本可用，该项目将建立在回归和成对图结构学习中的结构估计的最新进展的基础上，开发新的方法来进行结构估计和相关的推理，具有高阶依赖关系的模型。特别是，这项工作将集中在结构约束或正则化的估计，可以估计复杂的依赖关系，包括重叠和块相关的模式。对于推理和模式完成，重点将是基于约束优化和相关思想的新随机块更新的近似推理。

The ability to find patterns --- groups of variables working together --- and their dependencies in high dimensional problems are becoming crucially important in a wide variety of scientific, societal, and commercial applications. Important areas include cancer genomics, climate science, forest ecology, healthcare, and social media analytics. Typical patterns involve one or more groups of variables jointly exhibiting similar or dependent behavior in certain situations. In a predictive setting, activation of certain groups of variables often serves as a key signal for the prediction task. There is an urgent need for probabilistic models which go beyond identifying pairwise interactions, to understand higher order interactions between variables. Towards this end, the project will investigate novel methods based on structurally constrained dependency estimation and high-dimensional inference in probabilistic graphical models. This work will consider two important applications: climate and home care. Across the globe, climate change is impacting both the frequency and intensity of weather events, such as precipitation. The proposed methods will enable more accurate modeling of precipitation driven hydrological events. In the US, health care expenditures are expected to increase to 19.6% of the Gross Domestic Product (GDP) by 2019. The proposed work in home care is unique in scope and will be broadly applicable to any health care data, thus providing a foundation for future meaningful use of electronic health records, a national priority in the US. This project naturally spawns many educational opportunities, and will engage students through classroom teaching and associated modalities. The project will engage under-represented groups in the research, and disseminate the findings through workshops and tutorials.From a technical perspective, there are two central challenges for probabilistic pattern analysis with higher-order interactions: the combinatorial challenge, as one has to potentially look at all possible subsets of variables and their interactions, and the statistical challenge, as one typically has a small number of samples available, which can be unsuitable for testing significance of dependencies or relations found. The project will build on recent advances in structured estimation in regression and pairwise graph structure learning to develop novel approaches to structure estimation and associated inference for graphical models with higher order dependencies. In particular, the work will focus on estimation with structural constraints or regularization which can estimate complex dependencies, including overlapping and block-correlated patterns. For inference and pattern completion, the focus will be on approximate inference based on novel randomized block updates for constrained optimization and associated ideas.