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SUMMARY:Graphical models of local independence in stochastic processes
DTSTART:20231006T151500
DTEND:20231006T170000
DTSTAMP:20260930T194631Z
UID:917321a7bcce7e7750c2dd355e96dfb23557c88652935a2d9109d9ba
CATEGORIES:Conferences - Seminars
DESCRIPTION:Søren Wengel Mogensen\, Lund University and the University of
  Copenhagen\nGraphs are often used as representations of conditional indep
 endence structures of random vectors. In stochastic processes\, one may us
 e graphs to represent so-called local independence. Local independence is 
 an asymmetric notion of independence which describes how a system of stoch
 astic processes (e.g.\, point processes or diffusions) evolves over time. 
 Let A\, B\, and C be three subsets of the coordinate processes of the stoc
 hastic system. Intuitively speaking\, B is locally independent of A given 
 C if at every point in time knowing the past of both A and C is not more i
 nformative about the present of B than knowing the past of C only. Directe
 d graphs can be used to describe the local independence structure of the s
 tochastic processes using a separation criterion which is analogous to d-s
 eparation. In such a local independence graph\, each node represents an en
 tire coordinate process rather than a single random variable.\n\nIn this t
 alk\, we will describe various properties of graphical models of local ind
 ependence and then turn our attention to the case where the system is only
  partially observed\, i.e.\, some coordinate processes are unobserved. In 
 this case\, one can use so-called directed mixed graphs to describe the lo
 cal independence structure of the observed coordinate processes. Several d
 irected mixed graphs may describe the same local independence model\, and 
 therefore it is of interest to characterize such equivalence classes of di
 rected mixed graphs. It turns out that directed mixed graphs satisfy a cer
 tain maximality property which allows one to construct a simple graphical 
 representation of an entire Markov equivalence class of marginalized local
  independence graphs. This is convenient as the equivalence class can be l
 earned from data and its graphical representation concisely describes what
  underlying structure could have generated the observed local independenci
 es.\n\nDeciding Markov equivalence of two directed mixed graphs is computa
 tionally hard\, and we introduce a class of equivalence relations that are
  weaker than Markov equivalence\, i.e.\, lead to larger equivalence classe
 s. The weak equivalence classes enjoy many of the same properties as the M
 arkov equivalence classes\, and they provide a computationally feasible fr
 amework while retaining a clear interpretation. We discuss how this can be
  used for graphical modeling and causal structure learning based on local 
 independence.\n 
LOCATION:MA A3 31 https://plan.epfl.ch/?room==MA%20A3%2031
STATUS:CONFIRMED
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