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Abstract:
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In recent years, much work has been done in statistics on the estimation of network structure. Network structure can be defined in many ways, such as by sparse covariance matrices (encoding marginal associations), precision matrices (describing conditional associations) or by correlation matrices. Considerable work has been done in all of these settings for the estimation of the structure of a single network, and estimating the structure of multiple, related networks has been well studied in the sparse covariance and precision matrix settings. We develop a novel factor analysis approach to estimating the structure of related covariance matrices. We present the theoretical framework for the model, anchoring the model in a biological context. Results of the method applied to a lipidomics dataset are presented, and we conclude with an overview of model extensions.
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