Incorporating Knowledge into Structural Equation Models using Auxiliary Variables
This work addresses the challenge of integrating prior knowledge into causal inference models, offering an incremental improvement for researchers in statistics and machine learning.
The paper tackles the problem of incorporating background knowledge into structural equation models by proposing auxiliary variables that cancel paths, enabling improved identification and testing. The method identifies at least as many models as the most general existing technique for linear systems.
In this paper, we extend graph-based identification methods by allowing background knowledge in the form of non-zero parameter values. Such information could be obtained, for example, from a previously conducted randomized experiment, from substantive understanding of the domain, or even an identification technique. To incorporate such information systematically, we propose the addition of auxiliary variables to the model, which are constructed so that certain paths will be conveniently cancelled. This cancellation allows the auxiliary variables to help conventional methods of identification (e.g., single-door criterion, instrumental variables, half-trek criterion), as well as model testing (e.g., d-separation, over-identification). Moreover, by iteratively alternating steps of identification and adding auxiliary variables, we can improve the power of existing identification methods via a bootstrapping approach that does not require external knowledge. We operationalize this method for simple instrumental sets (a generalization of instrumental variables) and show that the resulting method is able to identify at least as many models as the most general identification method for linear systems known to date. We further discuss the application of auxiliary variables to the tasks of model testing and z-identification.