Convex Modeling with Priors

As the study of complex interconnected networks becomes widespread across disciplines, modeling the large-scale behavior of these systems becomes both increasingly important and increasingly difficult. In particular, it is of tantamount importance to utilize available prior information about the system's structure when building data-driven models of complex behavior. This thesis provides a framework for building models that incorporate domain specific knowledge and glean information from unlabelled data points. I present a methodology to augment standard methods in statistical regression with priors. These priors might include how the output series should behave or the specifics of the functional form relating inputs to outputs. My approach is optimization driven: by for-mulating a concise set of goals and constraints, approximate models may be systematically derived. The resulting approximations are convex and thus have only global minima and can be solved efficiently. The functional relationships amongst data are given as sums of nonlinear kernels that are expressive enough to approximate any mapping. Depending on the specifics of the prior, different estimation algorithms can be derived, and relationship