Causal Structure Learning from Sparse High Dimensional Data

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This research program studies causal learning in complex natural systems. The foundational challenge lies in inferring links in a high dimensional network based on limited observed data. For example, which genes can best prevent boar taint (an off-taste in pork meat)? Which regions of the brain are associated with cognitive function? Alternatively, what are the plant and pollinator traits driving plant and pollinator interactions? Can we predict interactions? Global concerns such as climate change, disease control, food security, and environmental management are replete with open problems. A general solution does not exist. Our approach is to develop powerful learning algorithms that can help researchers unlock these relationships. Animal breeding programs often require learning the structure of large genetic networks and identifying candidates for genetic selection. Consider boar taint, which is caused by high levels of two compounds. Candidate targets would be genes that reduce levels of one compound without adversely affecting fertility or production traits. The doubly sparse regression incorporating graphical structure of predictors (DSRIG) model leverages the (undirected) graph structure over predictors (gene expression levels) to improve prediction for a quantitative trait (boar taint). However, DSRIG is computationally intensive and does not distinguish between potential predictors that influence the response versus variables influenced by the response. Conservation management programs require learning the drivers of link formation, such as plant and pollinator species traits relevant to pollination. Anticipating which plant and pollinator species are most vulnerable to extinction or identifying species important in structuring the community can inform resource management and allocation efforts. Regularized grouped Dirichlet-multinomial (DM) regression is a consumer-resource model that models plant-pollinator interactions as a function of plant and pollinator traits. Unfortunately, survey data often underrepresent or exclude rare interactions. There is no established method to incorporate environmental covariates in the model or compare community structures across networks. The main objectives of the proposed program are to extend 1. the DSRIG framework to the causal (directed) graph setting, and 2. the grouped DM framework to compare networks over space or time. Short term goals include improving optimization of DSRIG; exploiting the directed structure of the predictor graph for a univariate response; extending the DM regression framework for zero-inflation; and comparing two networks over a (e.g., soil) gradient. Long term goals include extending DSRIG to the directed multivariate response setting and modelling bipartite networks more broadly over space and time. This research would benefit Canadian genetic selection and animal health monitoring programs as well as inform conservation and resource management practices.