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Determinantal generalizations of instrumental variables (2017)
Journal Article
Weihs, L., Robinson, B., Dufresne, E., Kenkel, J., Kubjas, K., McGee, R. L. I., …Drton, M. (2018). Determinantal generalizations of instrumental variables. Journal of Causal Inference, 6(1), doi:10.1515/jci-2017-0009. ISSN 2193-3685

Linear 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 vec... Read More

Mapping toric varieties into low dimensional spaces (2016)
Journal Article
Dufresne, E., & Jeffries, J. (in press). Mapping toric varieties into low dimensional spaces. Transactions of the American Mathematical Society, doi:10.1090/tran/7026. ISSN 0002-9947

A smooth d-dimensional projective variety X can always be embedded into 2d + 1-dimensional space. In contrast, a singular variety may require an arbitrary large ambient space. If we relax our requirement and ask only that the map is injective, then a... Read More

Invariants and separating morphisms for algebraic group actions (2015)
Journal Article
Dufresne, E., & Kraft, H. (2015). Invariants and separating morphisms for algebraic group actions. Mathematische Zeitschrift, 280(1-2), doi:10.1007/s00209-015-1420-0. ISSN 0025-5874

The first part of this paper is a refinement of Winkelmann’s work on invariant rings and quotients of algebraic group actions on affine varieties, where we take a more geometric point of view. We show that the (algebraic) quotient X//G given by the p... Read More