Improving identification algorithms in causal inference
Causal models provide a formal approach to the study of causality. One of the most useful features of causal modeling is that it enables one to make causal claims about a phenomenon using observational data alone under suitable conditions. This feature enables the analysis of interventions that may be infeasible to conduct in the real world for practical or ethical reasons. The uncertainty associated with the variables of interest is taken into account by including a probability distribution in the causal model, making it is possible to study the eﬀects of external interventions by examining how this distribution is changed by the action. The probability distribution of a speciﬁc variable in a causal model perturbed by an outside intervention is the causal eﬀect of that intervention on the variable. One of the most fundamental problems of causal inference is determining whether a causal eﬀect can be uniquely expressed in terms of the joint probability distribution over the observed variables in a given causal model. Causal eﬀects that can be expressed in this way are called identiﬁable and they serve as the link between observational and experimental information. Complete solutions to the identiﬁability problem take the form of an algorithm that produces an expression in terms of observed quantities whenever the causal eﬀect given as input is identiﬁable. However, completeness in this context refers only to the correctness and exhaustiveness of the methods. The formulas obtained as output from identiﬁability algorithms are often impractical and unnecessarily complicated. The thesis augments the pre-existing identiﬁability methodology by providing a simpliﬁcation procedure that drastically improves the complicated outputs in many cases. Simpliﬁcation also has practical beneﬁts when statistical estimation is considered if variables aﬀected by bias or missing data no longer appear in the simpliﬁed expression. The thesis also introduces a new method called pruning, which aims to eliminate variables that are unnecessary for the identiﬁcation task from the causal model itself. Finally, a variety of identiﬁcation algorithms are implemented more complicated settings, such as when data are available from multiple domains. The methods are provided through the R package “causaleﬀect” ...
PublisherUniversity of Jyväskylä
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