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Kernel Methods for Multistage Causal Inference: Mediation Analysis and Dynamic Treatment Effects
Rahul Singh · Liyuan Xu · Arthur Gretton

We propose kernel ridge regression estimators for causal inference in multistage settings. Specifically, we focus on (i) the decomposition of a total effect into a direct effect and an indirect effect (mediated by a particular mechanism); and (ii) effects of sequences of treatments. We allow treatment, covariates, and mediators to be discrete or continuous, and low, high, or infinite dimensional. We propose estimators of means, increments, and distributions of counterfactual outcomes. Important examples are (i) direct and indirect dose response curves; and (ii) dynamic dose response curves. Each estimator has a closed form solution and is easily computed by kernel matrix operations. For the nonparametric case, we prove uniform consistency and provide finite sample rates of convergence. For the semiparametric case, we prove root-n consistency, Gaussian approximation, and semiparametric efficiency. We evaluate our estimators in simulations then estimate mediated and dynamic treatment effects of the US Job Corps training program for disadvantaged youth.

Author Information

Rahul Singh (MIT)

Rahul Singh is a PhD candidate in Economics and Statistics at MIT. His research interests are causal inference and statistical learning theory.

Liyuan Xu (UCL)
Arthur Gretton (Gatsby Unit, UCL)

Arthur Gretton is a Professor with the Gatsby Computational Neuroscience Unit at UCL. He received degrees in Physics and Systems Engineering from the Australian National University, and a PhD with Microsoft Research and the Signal Processing and Communications Laboratory at the University of Cambridge. He previously worked at the MPI for Biological Cybernetics, and at the Machine Learning Department, Carnegie Mellon University. Arthur's recent research interests in machine learning include the design and training of generative models, both implicit (e.g. GANs) and explicit (high/infinite dimensional exponential family models), nonparametric hypothesis testing, and kernel methods. He has been an associate editor at IEEE Transactions on Pattern Analysis and Machine Intelligence from 2009 to 2013, an Action Editor for JMLR since April 2013, an Area Chair for NeurIPS in 2008 and 2009, a Senior Area Chair for NeurIPS in 2018, an Area Chair for ICML in 2011 and 2012, and a member of the COLT Program Committee in 2013. Arthur was program chair for AISTATS in 2016 (with Christian Robert), tutorials chair for ICML 2018 (with Ruslan Salakhutdinov), workshops chair for ICML 2019 (with Honglak Lee), program chair for the Dali workshop in 2019 (with Krikamol Muandet and Shakir Mohammed), and co-organsier of the Machine Learning Summer School 2019 in London (with Marc Deisenroth).

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