Bayesian estimation of causal effects from observational categorical data

We present a Bayesian procedure for estimation of pairwise intervention effects in a high-dimensional system of categorical variables. We assume that we have observational data generated from an unknown causal Bayesian network for which there are no latent confounders. Most of the existing methods developed for this setting assume that the underlying model is linear Gaussian, including the Bayesian IDA (BIDA) method that we build upon in this work. By combining a Bayesian backdoor estimator with model averaging, we obtain a posterior over the intervention distributions of a cause-effect pair that can be expressed as a mixture over stochastic linear combinations of Dirichlet distributions. Although there is no closed-form expression for the posterior density, it is straightforward to produce Monte Carlo approximations of target quantities through direct sampling, and we also derive closed-form expressions for a few selected moments. To scale up the proposed procedure, we employ Markov Chain Monte Carlo (MCMC), which also enables us to use more efficient adjustment sets compared to the current exact BIDA. Finally, we use Jensen-Shannon divergence to define a novel causal effect based on a set of intervention distributions in the general categorical setting. We compare our method to the original IDA method and existing Bayesian approaches in numerical simulations and show that categorical BIDA performs favorably against the existing alternative methods in terms of producing point estimates and discovering strong effects.