Toric invariant theory for maximum likelihood estimation in log-linear models

14 Dec 2020 · Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, Anna Seigal ·

We establish connections between invariant theory and maximum likelihood estimation for discrete statistical models. We show that norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We use notions of stability under a torus action to characterize the existence of the maximum likelihood estimate, and discuss connections to scaling algorithms.

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Toric invariant theory for maximum likelihood estimation in log-linear models

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