## Statistical Analysis of Metric Graph Reconstruction

*Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman*; 15(Oct):3425−3446, 2014.

### Abstract

A metric graph is a 1-dimensional stratified metric space
consisting of vertices and edges or loops glued together. Metric
graphs can be naturally used to represent and model data that
take the form of noisy filamentary structures, such as street
maps, neurons, networks of rivers and galaxies. We consider the
statistical problem of reconstructing the topology of a metric
graph embedded in $\mathbb{R}^D$ from a random sample. We derive
lower and upper bounds on the minimax risk for the noiseless
case and tubular noise case. The upper bound is based on the
reconstruction algorithm given in Aanjaneya et al. (2012).

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