[Facets-of-complexity] Invitation to Monday's Lecture & Colloquium Feb.14 - online via Zoom.

["I.Brunke" <i.brunke@fu-berlin.de>]

Dear all,

next Monday's Lecture and Colloquium will take place online via Zoom on February 14.

Please find link to Zoom Meeting here:

https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09

A password is not required!

You all are cordially invited!

Location:

Online via Zoom.

Monday's Lecture: Carlos Amendola (Technische Universität München)

Time: Monday, February 14 - 14:15 h

Title: Estimating Gaussian mixtures using sparse polynomial moment systems

Abstract:

The method of moments is a statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A fundamental question critical to understanding identifiability asks how many moment equations are needed to get finitely many solutions and how many solutions there are. 

Since the moments of a mixture of Gaussians are polynomial expressions in the means, variances and mixture weights, one can address this question from the perspective of algebraic geometry. With the help of tools from polyhedral geometry, we answer this fundamental question for several classes of Gaussian mixture models. Furthermore, these results allow us to present an algorithm that performs parameter recovery and density estimation, applicable even in the high dimensional case.

Based on joint work with Julia Lindberg and Jose Rodriguez (University of Wisconsin-Madison).

Break

Monday's Colloquium: Marie Brandenburg (Max Planck Institut Leipzig)

Time: Monday, February 14 - 16:00 h s.t.

Title: Intersection Bodies of Polytopes

Abstract:

Intersection bodies are classical objects from convex geometry, that are constructed from given convex body. In the past, they have mainly been studied from the point of view of convex analysis. In this talk we investigate combinatorial and algebraic structures of intersection bodies of polytopes. We consider an algorithm to compute both the radial function and the algebraic boundary of these intersection bodies, and provide an upper bound for their degree. This is joint work with Katalin Berlow, Chiara Meroni and Isabelle Shankar.

You all are cordially invited!

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