Counterfactual Distribution Regression for Structured Inference
This addresses inference challenges for systems subject to external perturbations, like transportation networks, but appears incremental as it builds on existing distribution regression methods.
The paper tackles the problem of predicting system behavior changes due to novel perturbations, such as disruptions in a train network affecting passenger traffic, by developing a variant of distribution regression that maps from counterfactual to disrupted distributions.
We consider problems in which a system receives external \emph{perturbations} from time to time. For instance, the system can be a train network in which particular lines are repeatedly disrupted without warning, having an effect on passenger behavior. The goal is to predict changes in the behavior of the system at particular points of interest, such as passenger traffic around stations at the affected rails. We assume that the data available provides records of the system functioning at its "natural regime" (e.g., the train network without disruptions) and data on cases where perturbations took place. The inference problem is how information concerning perturbations, with particular covariates such as location and time, can be generalized to predict the effect of novel perturbations. We approach this problem from the point of view of a mapping from the counterfactual distribution of the system behavior without disruptions to the distribution of the disrupted system. A variant on \emph{distribution regression} is developed for this setup.