DACO seminar

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Datum / Zeit

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Titel

Ort

20. März 2025
14:15-15:15

Dr. Léo Mathis
Goethe University Frankfurt, DE

Details

Titel	Non centered Gaussian determinants with Gaussian zonoids
Referent:in, Affiliation	Dr. Léo Mathis, Goethe University Frankfurt, DE
Datum, Zeit	20. März 2025, 14:15-15:15
Ort	HG G 19.1
Abstract	A Theorem of Vitale, Molchanov and Wespi, states that the expected absolute determinant of a random matrix with independent columns is equal to the mixed volume of some convex bodies called zonoids. In the case where the columns of the matrix are centered Gaussian, the corresponding zonoids are ellipsoids and this was studied by Kabluchko and Zaporozhets. The case of non centered Gaussian vectors, however, remains relatively unstudied. The convex bodies we obtain in this case, which I call Gaussian zonoids, are not ellipsoids. In this talk, I will show you what a Gaussian zonoid looks like and how one can approximate it with an ellipsoid. At the level of random determinants, this allows to approximate expectation of non centered Gaussian determinants with centered ones. If time allows, I will show how this applies to Gaussian random fields. Namely, I will show how one can give a quantitative estimate of the concentration of a small Gaussian perturbation of a hypersurface.

Non centered Gaussian determinants with Gaussian zonoidsread_more

27. März 2025
14:15-15:15

Prof. Dr. Irene Waldspurger
CEREMADE (Université Paris-Dauphine)

Details

Titel	Correctness guarantees for the Burer-Monteiro heuristic on MaxCut-type problems
Referent:in, Affiliation	Prof. Dr. Irene Waldspurger, CEREMADE (Université Paris-Dauphine)
Datum, Zeit	27. März 2025, 14:15-15:15
Ort	HG G 19.1
Abstract	Since numerically solving high-dimensional semidefinite programs is challenging, solvers should exploit the structure of the problem at hand, when it allows for speedups. In this talk, we will consider the setting where we have the a priori information that the solution is of low rank (for instance, rank 1). A standard way to exploit this information is through the Burer-Monteiro factorization: we represent the unknown matrix as a product of "thin" matrices (i.e. with few columns); then, we optimize the factors instead of the whole square matrix. This technique reduces the dimensionality of the problem, allowing for important computational savings. However, it makes the problem non-convex, thereby possibly introducing non-optimal critical points which can cause the solver to fail. With Faniriana Rakoto Endor, we have considered the specific category of so-called "MaxCut-type" semidefinite problems. We have exhibited a simple property which guarantees that the resulting non-convex problem has no non-optimal critical point, and hence ensures the success of the algorithm.

Correctness guarantees for the Burer-Monteiro heuristic on MaxCut-type problemsread_more

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