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pro vyhledávání: '"20G45"'
In this note we prove that a finite family $\{X_1,\dots,X_d\}$ of real r.v.'s that is exchangeable and such that $(X_1,\dots,X_d)$ is invariant with respect to a subgroup of $SO(d)$ acting irreducibly, is actually invariant with respect to the action
Externí odkaz:
http://arxiv.org/abs/2310.19611
Autor:
Jakobsen, Hans Plesner
We construct homomorphic images of $su(n,n)^{\mathbb C}$ in Weyl Algebras ${\mathcal H}_{2nr}$. More precisely, and using the Bernstein filtration of ${\mathcal H}_{2nr}$, $su(n,n)^{\mathbb C}$ is mapped into degree $2$ elements with the negative non
Externí odkaz:
http://arxiv.org/abs/2111.03378
We define Gaussian graphical models on directed acyclic graphs with coloured vertices and edges, calling them RDAG (restricted directed acyclic graph) models. If two vertices or edges have the same colour, their parameters in the model must be the sa
Externí odkaz:
http://arxiv.org/abs/2108.10058
Publikováno v:
Alg. Stat. 12 (2021) 187-211
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
Externí odkaz:
http://arxiv.org/abs/2012.07793
Publikováno v:
Forum of Mathematics, Sigma, 10, E50 (2022)
In this paper, we study sample size thresholds for maximum likelihood estimation for tensor normal models. Given the model parameters and the number of samples, we determine whether, almost surely, (1) the likelihood function is bounded from above, (
Externí odkaz:
http://arxiv.org/abs/2011.03849
Autor:
Derksen, Harm, Makam, Visu
In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number of samples needed to achieve (almost surely) three conditions, namely
Externí odkaz:
http://arxiv.org/abs/2007.10206
Publikováno v:
J. Math. Phys. 62, 021701 (2021)
This work is motivated by the relation between the KP and BKP integrable hierarchies, whose $\tau$-functions may be viewed as sections of dual determinantal and Pfaffian line bundles over infinite dimensional Grassmannians. In finite dimensions, we s
Externí odkaz:
http://arxiv.org/abs/2007.03586
Autor:
Gourevitch, Dmitry, Gustafsson, Henrik P. A., Kleinschmidt, Axel, Persson, Daniel, Sahi, Siddhartha
We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also
Externí odkaz:
http://arxiv.org/abs/2004.14244
We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We focus on Gaussian transformation families, which include matrix normal models and Gaussian graphical models gi
Externí odkaz:
http://arxiv.org/abs/2003.13662
Autor:
Jakobsen, Hans Plesner
We study homomorphisms between quantized generalized Verma modules $M(V_{\Lambda})\stackrel{\phi_{\Lambda,\Lambda_1}}{\rightarrow}M(V_{\Lambda_1})$ for ${\mathcal U}_q(su(n,n))$. There is a natural notion of degree for such maps, and if the map is of
Externí odkaz:
http://arxiv.org/abs/1905.04491