Do-calculus enables causal reasoning with latent variable models

Latent variable models (LVMs) are probabilistic models where some of the variables are hidden during training. A broad class of LVMshave a directed acyclic graphical structure. The directed structure suggests an intuitive causal explanation of the data generating process. For example, a latent topic model suggests that topics cause the occurrence of a token. Despite this intuitive causal interpretation, a directed acyclic latent variable model trained on data is generally insufficient for causal reasoning, as the required model parameters may not be uniquely identified. In this manuscript we demonstrate that an LVM can answer any causal query posed post-training, provided that the query can be identified from the observed variables according to the do-calculus rules. We show that causal reasoning can enhance a broad class of LVM long established in the probabilistic modeling community, and demonstrate its effectiveness on several case studies. These include a machine learning model with multiple causes where there exists a set of latent confounders and a mediator between the causes and the outcome variable, a study where the identifiable causal query cannot be estimated using the front-door or back-door criterion, a case study that captures unobserved crosstalk between two biological signaling pathways, and a COVID-19 expert system that identifies multiple causal queries.