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Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming

Abstract : We establish connections between: the maximum likelihood degree (ML-degree) for linear concentration models, the algebraic degree of semidefinite programming (SDP), and Schubert calculus for complete quadrics. We prove a conjecture by Sturmfels and Uhler on the polynomiality of the ML-degree. We also prove a conjecture by Nie, Ranestad and Sturmfels providing an explicit formula for the degree of SDP. The interactions between the three fields shed new light on the asymptotic behaviour of enumerative invariants for the variety of complete quadrics. We also extend these results to spaces of general matrices and of skew-symmetric matrices.
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Preprints, Working Papers, ...
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https://hal-cnrs.archives-ouvertes.fr/hal-03816255
Contributor : Laurent Manivel Connect in order to contact the contributor
Submitted on : Saturday, October 15, 2022 - 10:28:25 PM
Last modification on : Tuesday, October 25, 2022 - 11:58:11 AM

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  • HAL Id : hal-03816255, version 1
  • ARXIV : 2011.08791

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Laurent Manivel, Mateusz Michałek, Leonid Monin, Tim Seynnaeve, Martin Vodička. Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming. {date}. ⟨hal-03816255⟩

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