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SUMMARY:Measuring statistical dependency with optimal transport
DTSTART;VALUE=DATE-TIME:20220804T133000Z
DTEND;VALUE=DATE-TIME:20220804T135000Z
DTSTAMP;VALUE=DATE-TIME:20231210T041653Z
UID:indico-contribution-1222@conference2.aau.at
DESCRIPTION:In this talk\, we introduce a novel framework for measuring st
atistical dependency between two random variables $X$ and $Y$\, the *trans
port dependency* $\\tau(X\, Y) \\ge 0$. This coefficient relies on the not
ion of optimal transport and is applicable to random variables\, taking va
lues in general Polish spaces. It can be estimated consistently via the co
rresponding empirical measure\, is versatile and adaptable to various scen
arios by proper choices of the cost function\, and intrinsically respects
metric properties of the ground spaces. Notably\, statistical independence
is characterized by $\\tau(X\, Y) = 0$\, while large values of $\\tau(X\,
Y)$ indicate highly regular relations between $X$ and $Y$. Indeed\, for s
uitable base costs\, $\\tau(X\, Y)$ is maximized if and only if $Y$ can be
expressed as 1-Lipschitz function of $X$ or vice versa.\nWe exploit this
characterization and define a class of dependency coefficients with values
in $[0\, 1]$\, which can emphasizes different functional relations. In p
articular\, for suitable costs the *transport correlations* is symmetric a
nd attains the value $1$ if and only if $Y = f(X)$ where $f$ is a multiple
of an isometry\, which makes it comparable to the distance correlation.\n
Finally we illustrate how the transport dependency can be used in practice
to explore dependencies between random variables\, in a gene expression s
tudy.\n\nhttps://conference2.aau.at/event/131/contributions/1222/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1222/
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