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SUMMARY:Model-oriented Graph Distances via Partially Ordered Sets - Richar
 d Guo (University of Michigan)
DTSTART:20260302T104500Z
DTEND:20260302T113000Z
UID:TALK244354@talks.cam.ac.uk
DESCRIPTION:A well-defined distance on the parameter space is key to evalu
 ating estimators\, ensuring consistency\, and building confidence sets. Wh
 ile there are typically standard distances to adopt in a continuous space\
 , this is not the case for combinatorial parameters such as graphs that re
 present statistical models. Defined on the graphs alone\, existing proposa
 ls like the structural Hamming distance ignore the structure of the model 
 space and can thus exhibit undesirable behaviors. We propose a model-orien
 ted framework for defining the distance between graphs that is applicable 
 across different graph classes. Our approach treats each graph as a statis
 tical model and organizes the graphs in a partially ordered set based on m
 odel inclusion. This induces a neighborhood structure\, from which we defi
 ne the model-oriented distance as the length of a shortest path through ne
 ighbors\, yielding a metric in the space of graphs. We apply this framewor
 k to probabilistic undirected graphs\, causal directed acyclic graphs\, pr
 obabilistic completed partially directed acyclic graphs\, and causal maxim
 ally oriented partially directed acyclic graphs. We analyze the theoretica
 l and empirical behaviors of model-oriented distances and draw comparison 
 with existing distances. Algorithmic tools are also developed for computin
 g and bounding our distances.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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