### Browsing by Author "Robeva, Elina"

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Item Determinantal Generalizations of Instrumental Variables(DE GRUYTER, 2018-03) Weihs, Luca; Robinson, Bill; Dufresne, Emilie; Kenkel, Jennifer; Kubjas, Kaie; McGee, Reginald L., II; Nguyen, Nhan; Robeva, Elina; Drton, Mathias; University of Washington; Denison University; University of Nottingham; University of Utah; Statistics and Mathematical Data Science; Ohio State University; University of Montana; Massachusetts Institute of Technology MIT; Department of Mathematics and Systems AnalysisLinear structural equation models relate the components of a random vector using linear interdependencies and Gaussian noise. Each such model can be naturally associated with a mixed graph whose vertices correspond to the components of the random vector. The graph contains directed edges that represent the linear relationships between components, and bidirected edges that encode unobserved confounding. We study the problem of generic identifiability, that is, whether a generic choice of linear and confounding effects can be uniquely recovered from the joint covariance matrix of the observed random vector. An existing combinatorial criterion for establishing generic identifiability is the half-trek criterion (HTC), which uses the existence of trek systems in the mixed graph to iteratively discover generically invertible linear equation systems in polynomial time. By focusing on edges one at a time, we establish new sufficient and necessary conditions for generic identifiability of edge effects extending those of the HTC. In particular, we show how edge coefficients can be recovered as quotients of subdeterminants of the covariance matrix, which constitutes a determinantal generalization of formulas obtained when using instrumental variables for identification.Item Positive semidefinite rank and nested spectrahedra(TAYLOR & FRANCIS LTD, 2018) Kubjas, Kaie; Robeva, Elina; Robinson, Richard Z.; Statistics and Mathematical Data Science; Massachusetts Institute of Technology MIT; University of Washington; Department of Mathematics and Systems AnalysisThe set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general values of positive semidefinite rank we provide a conjecture for the description of this boundary. Our proof techniques are geometric in nature and rely on nesting spectrahedra between polytopes.