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.
