Function Driven Diffusion for Personalized Counterfactual Inference

10/31/2016

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by   Alexander Cloninger, et al.

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We consider the problem of constructing diffusion operators high dimensional data X to address counterfactual functions F, such as individualized treatment effectiveness. We propose and construct a new diffusion metric K_F that captures both the local geometry of X and the directions of variance of F. The resulting diffusion metric is then used to define a localized filtration of F and answer counterfactual questions pointwise, particularly in situations such as drug trials where an individual patient's outcomes cannot be studied long term both taking and not taking a medication. We validate the model on synthetic and real world clinical trials, and create individualized notions of benefit from treatment.