Counterfactual analyses with graphical models based on local independence
By K. Røysland. 2011
30 citations recorded by the source corpus.
We show that one can perform causal inference in a natural way for continuous-time scenarios using tools from stochastic analysis. This provides new alternatives to the positivity condition for inverse probability weighting. The probability distribution that would govern the frequency of observations in the counterfactual scenario can be characterized in terms of a so-called martingale problem. The counterfactual and factual probability distributions may be related through a likelihood ratio given by a stochastic differential equation. We can perform inference for counterfactual scenarios based on the original observations, re-weighted according to this likelihood ratio. This is possible if the solution of the stochastic differential equation is uniformly integrable, a property that can be determined by comparing the corresponding factual and counterfactual short-term predictions. Local independence graphs are directed, possibly cyclic, graphs that represent short-term prediction among sufficiently autonomous stochastic processes. We show through an example that these graphs can be used to identify and provide consistent estimators for counterfactual parameters in continuous time. This is analogous to how Judea Pearl uses graphical information to identify causal effects in finite state Bayesian networks.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Molecular Biology
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Citations in the corpus
- Can we believe the DAGs? A comment on the relationship between causal DAGs and mechanisms (2014, background): “For a study of causal models with local independence, see Røysland.”
- Markov equivalence of marginalized local independence graphs (2018, unknown): “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].”