Graphical models for marked point processes based on local independence

By Vanessa Didelez. 2007

175 citations recorded by the source corpus.

Summary. A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so‐called local independences, meaning that the intensities of certain types of events are independent of some (but not necessarilly all) events in the past. This dynamic concept of independence is asymmetric, similar to Granger non‐causality, so the corresponding local independence graphs differ considerably from classical graphical models. Hence a new notion of graph separation, which is called δ‐separation, is introduced and implications for the underlying model as well as for likelihood inference are explored. Benefits regarding facilitation of reasoning about and understanding of dynamic dependences as well as computational simplifications are discussed.

Subfields: Artificial Intelligence, Computer Networks and Communications

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Citations in the corpus

Causal Models for Dynamical Systems (2020, neutral): “For speciﬁc model classes, there is interesting work exploiting the concept of local independence [Schweder, 1970, Mogensen et al., 2018, Mogensen and Hansen, 2019, Didelez, 2000, 2008], with several questions still being open.”
Causal interpretation of stochastic differential equations (2013, background): “mework can be found in [17, 15, 6]. One of the most recent frameworks for causality in continuous time is based on the concept of weak conditional local independence. For results related to this, see [8, 5, 16, 32, 33]. An alternative notion of causality deﬁned solely through ﬁltrations is developed”
Causality, mediation and time: a dynamic viewpoint (2012, background): “There is an analogous concept for local independence graphs called δ-separation which was developed by Didelez (2008).”
Markov equivalence of marginalized local independence graphs (2018, methodology): “Several authors have since then used graphs to represent local independence structures of multivariate stochastic process models, in particular for point process models; see, for example, [4, 11–13 , 35].”
Counterfactual analyses with graphical models based on local independence (2011, background): “Note also that graphical models based on local independence and doubly stochastic Poisson processes were studied thoroughly in [9].”
Causal Learning for Partially Observed Stochastic Dynamical Systems (2018, methodology): “We deﬁne the following properties, some of which have previously been described as asymmetric (semi)graphoid properties (Didelez, 2006b, 2008).”
Can we believe the DAGs? A comment on the relationship between causal DAGs and mechanisms (2014, background): “An important concept which has recently received increasing attention is that of local independence.(3,4,14) Local independence is a concept that looks at how well future values of a process can be predicted by past.”
Fast MCMC sampling for Markov jump processes and extensions (2012, methodology): “Here ‘time’ represents position along the strand, with particular ‘motifs’ occurring with different rates in different regions (Fearnhead and Sherlock, 2006). MJPs are also widely used in finance, for example, Elliott and Osakwe (2006) use an MJP to model switches in the parameters that govern the d”