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Linking Invariant Theory to Maximum Likelihood Estimation

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EMGW02 - Applied and computational algebraic geometry

We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. This will be illustrated in the two statistical settings of log-linear models and Gaussian transformation families.  The former includes the classical independence model while the latter includes matrix normal models and Gaussian graphical models given by transitive directed acyclic graphs. In particular, stability under group actions is used to characterize boundedness of the likelihood, and existence and uniqueness of the maximum likelihood estimate. Based on joint work with Kathlén Kohn, Philipp Reichenbach and Anna Seigal.

This talk is part of the Isaac Newton Institute Seminar Series series.

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