Inference of Causal Relations with Interventions

• Activity Number: 143 - New Machine Learning Tools for Mobile Health Data and Individual Intervention
• Type: Invited
• Date/Time: Tuesday, August 10, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Lifetime Data Science Section
• Author(s): Chunlin Li and Xiaotong T Shen* and Wei Pan
• Companies: University of Minnesota and University of Minnesota and University of Minnesota
• Keywords: High-dimensional inference; identifiability; testability; Likelihood ratio tests

Abstract

The inference of causal relations between primary variables is challenging in the presence of unknown interventions. In this article, we infer multiple causal relations while identifying relevant interventions. In particular, we derive conditions for multiple unknown interventions to yield an identifiable model. For inference, we need to identify the ancestral relations and the interventions for each hypothesis-specific primary variable. Towards this end, we propose a causal discoveryalgorithm. On this ground, we propose a likelihood ratio test based on data perturbation, in which the identification effect is accounted for by perturbing original data to assess the uncertainty associated with identifying ancestors and interventions. For testing the presence and strengths of causal relations in a pathway, we show that the proposed tests achieve desired statistical properties in terms of controlling Types I and II error in a higher-dimensional situation. Numerical examples will be given to demonstrate the utility and effectiveness of the proposed procedure.