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We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory.
Two new properties of mathematical likelihood
Ronald Aylmer Fisher · 1934
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The multivariate distribution of complex normal variables
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Graphical models
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On the Markov equivalence of chain graphs, undirected graphs, and acyclic digraphs
S.A. Andersson, D. Madigan, and M.D. Perlman · 1997
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Conditional iterative proportional fitting for gaussian distributions
Erhard Cramer · 1998
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The MLE algorithm for the matrix normal distribution
Pierre Dutilleul · 1999
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Tutorial on maximum likelihood estimation
I.J. Myung · 2003
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Classical complexity and quantum entanglement
L. Gurvits · 2004
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The likelihood ratio test for a separable covariance matrix
N. Lu and D.L. Zimmerman · 2005
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The Hilbert null-cone on tuples of matrices and bilinear forms
M. Bürgin and J. Draisma · 2006
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Wishart distributions for decomposable graphs
Polynomial degree bounds for matrix semi-invariants
H. Derksen and V. Makam · 2017
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Algebraic groups
J.S. Milne · 2017
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Geometric invariant theory: Over the real and complex numbers
N.R. Wallach · 2017
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Operator scaling via geodesically convex optimization, invariant theory and polynomial identity testing
Z. Allen-Zhu, A. Garg, Y. Li, R. Oliveira, and A. Wigderson · 2018
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Constructive non-commutative rank computation is in deterministic polynomial time
G. Ivanyos, Y. Qiao, and K.V. Subrahmanyam · 2018
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Algebraic Statistics
S. Sullivant · 2018
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Groups acting on Gaussian graphical models
J. Draisma, S. Kuhnt, and P. Zwiernik · 2013
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On optimization algorithms for maximum likelihood estimation
A.T. Mai, F. Bastin, and M. Toulouse · 2014
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A deterministic polynomial time algorithm for non-commutative rational identity testing
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Alternating minimization, scaling algorithms, and the null-cone problem from invariant theory
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Real geometric invariant theory
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P. Bürgisser, C. Franks, A. Garg, R. Oliveira, M. Walter, and A. Wigderson · 2019
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The maximum likelihood threshold of a path diagram
M. Drton, C. Fox, A. Käufl, and G. Pouliot · 2019
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Toric invariant theory for maximum likelihood estimation in log-linear models
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