  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.
