2015/11/10 by Bryant Chen, Judea Pearl, Chen, Bryant +3 · 1 citation
Computer Science · Mathematics · Biochemistry, Genetics and Molecular Biology · #Bayesian Modeling and Causal Inference #Advanced Causal Inference Techniques #Metabolomics and Mass Spectrometry Studies
paper · pdf · doi:10.48550/arxiv.1511.02995
In this paper, we extend graph-based identification methods by allowing\nbackground knowledge in the form of non-zero parameter values. Such information\ncould be obtained, for example, from a previously conducted randomized\nexperiment, from substantive understanding of the domain, or even an\nidentification technique. To incorporate such information systematically, we\npropose the addition of auxiliary variables to the model, which are constructed\nso that certain paths will be conveniently cancelled. This cancellation allows\nthe auxiliary variables to help conventional methods of identification (e.g.,\nsingle-door criterion, instrumental variables, half-trek criterion), as well as\nmodel testing (e.g., d-separation, over-identification). Moreover, by\niteratively alternating steps of identification and adding auxiliary variables,\nwe can improve the power of existing identification methods via a bootstrapping\napproach that does not require external knowledge. We operationalize this\nmethod for simple instrumental sets (a generalization of instrumental\nvariables) and show that the resulting method is able to identify at least as\nmany models as the most general identification method for linear systems known\nto date. We further discuss the application of auxiliary variables to the tasks\nof model testing and z-identification.\n