06.11.2024, 14:00 - 16:00
– Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium
Graphon Models for Inhomogeneous Random Graphs
Olga Klopp (Paris), Nicolas Verzelen (Montpellier)
Clément Berenfeld (UP)
Given i.i.d. random variables drawn from a mixture of immersed low-dimensional submanifolds of different dimensions, we study the minimax estimation of the family of submanifolds in Hausdorff distance. We provide a constructive algorithm allowing to estimate each mixture component at its optimal dimension-specific rate adaptively. The method is based on an ascending hierarchical co-detection of points belonging to different layers, which also identifies the number of layers, the dimensions of these layers, assign each data point to a layer accurately, and estimate tangent spaces optimally.
These results hold regardless of any reach assumption on the submanifolds or on their (auto) intersection configurations.
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