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SUMMARY:Identification in Graphical Continuous Lyapunov Models
DTSTART;VALUE=DATE-TIME:20220804T080000Z
DTEND;VALUE=DATE-TIME:20220804T082000Z
DTSTAMP;VALUE=DATE-TIME:20240915T094753Z
UID:indico-contribution-1215@conference2.aau.at
DESCRIPTION:Graphical continuous Lyapunov models offer a new perspective o
n modeling the causally interpretable dependence structure in multivariate
data by treating each independent observation as a one-time cross-section
al snapshot of the multivariate Ornstein-Uhlenbeck process in equilibrium.
This leads to Gaussian models in which the covariance matrix is determine
d by the continuous Lyapunov equation. In this setting\, each graphical mo
del assumes a sparse drift matrix with support determined by a directed gr
aph. We study the crucial problem of parameter identifiability in the clas
s of graphical continuous Lyapunov models. Indeed\, given a statistical mo
del induced by a graph\, it is essential for statistical analysis to clari
fy if it is possible to uniquely recover the parameters from the joint dis
tribution of the observed variables.\n\nWe show that this question can be
reduced to analyzing the rank of certain sparse matrices with covariances
as entries. Depending on the graph under consideration\, the structure of
these matrices changes in subtle ways. We study the identifiability for di
fferent classes of graphs. In our main result we prove that global identif
iability holds if and only if the graph is simple (i.e.\, contains at most
one edge between any two nodes). Furthermore\, we present intriguing exam
ples of non-simple graphs for which the associated model has generically i
dentifiable parameters.\n\nhttps://conference2.aau.at/event/131/contributi
ons/1215/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1215/
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