B1190
Title: Identifiability of cyclic linear structural equation models via algebraic matroids
Authors: Benjamin Hollering - TU Munich (Germany) [presenting]
Mathias Drton - Technical University of Munich (Germany)
Jun Wu - Technical University of Munich (Germany)
Abstract: Linear structural equation models associated with directed graphs are a common and applicable family of graphical models which have been studied extensively. One common assumption is that the underlying graph is acyclic, and in this setting, the identifiability of the graph has been long established. The identifiability of these models while the associated graph is allowed to be cyclic and the errors are homoscedastic is discussed. It is proven that several combinatorial conditions on graphs are sufficient for identifiability by examining the algebraic matroid of the statistical model. Based on these conditions, subclasses of graphs that allow for directed cycles yet are generically identifiable are exhibited. The study is supplemented by computational experiments that provide a full classification of models given by simple graphs with up to 6 nodes.
