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      Counterfactual Distribution Regression for Structured Inference

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          Abstract

          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.

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          Most cited references 9

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          A Hilbert Space Embedding for Distributions

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            Kernel Mean Embedding of Distributions: A Review and Beyond

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              Causal inference by using invariant prediction: identification and confidence intervals

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                Author and article information

                Journal
                20 August 2019
                Article
                1908.07193

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                24 pages, 5 figures
                cs.LG stat.AP stat.ME stat.ML

                Applications, Machine learning, Artificial intelligence, Methodology

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