Title: Obtaining Accurate Probabilistic Causal Inference by Post-Processing Calibration,
Abstract: Discovery of an accurate causal Bayesian network structure from observational
data can be useful in many areas of science. Often the discoveries are made
under uncertainty, which can be expressed as probabilities. To guide the use of
such discoveries, including directing further investigation, it is important
that those probabilities be well-calibrated. In this paper, we introduce a
novel framework to derive calibrated probabilities of causal relationships from
observational data. The framework consists of three components: (1) an
approximate method for generating initial probability estimates of the edge
types for each pair of variables, (2) the availability of a relatively small
number of the causal relationships in the network for which the truth status is
known, which we call a calibration training set, and (3) a calibration method
for using the approximate probability estimates and the calibration training
set to generate calibrated probabilities for the many remaining pairs of
variables. We also introduce a new calibration method based on a shallow neural
network. Our experiments on simulated data support that the proposed approach
improves the calibration of causal edge predictions. The results also support
that the approach often improves the precision and recall of predictions.