Graduate School and Research Center in Digital Sciences

Counterfactual mean embeddings

Muandet, Krikamol; Kanagawa, Motonobu; Saengkyongam, Sorawit; Marukatat, Sanparith

Submitted to ArXiV, 1st March 2020

Counterfactual inference has become a ubiquitous tool in online advertisement, recommendation systems, medical diagnosis, and finance. Accurate modeling of outcome distributions associated with different interventions---known as counterfactual distributions---is crucial for the success of these applications. In this work, we propose to model counterfactual distributions using a novel Hilbert space representation called counterfactual mean embedding (CME). The CME embeds the associated counterfactual distribution into a reproducing kernel Hilbert space (RKHS) endowed with a positive definite kernel, which allows us to perform causal inference over the entire landscape of the counterfactual distribution. Based on this representation, we propose a distributional treatment effect (DTE) which can quantify the causal effect over entire outcome distributions. Our approach is nonparametric as the CME can be estimated consistently from observational data without requiring any parametric assumption about the underlying distributions. We also establish a rate of convergence of the proposed estimator which depends on the smoothness of the conditional mean and the Radon-Nikodym derivative of the underlying marginal distributions. Furthermore, our framework also allows for more complex outcomes such as images, sequences, and graphs. Lastly, our experimental results on synthetic data and off-policy evaluation tasks demonstrate the advantages of the proposed estimator.    

Arxiv Bibtex

Title:Counterfactual mean embeddings
Keywords:Counterfactual Inference, Kernel Mean Embedding, Potential Outcome Framework, Reproducing Kernel Hilbert Space, Causality
Department:Data Science
Eurecom ref:6255
Copyright: © EURECOM. Personal use of this material is permitted. The definitive version of this paper was published in Submitted to ArXiV, 1st March 2020 and is available at :
Bibtex: @inproceedings{EURECOM+6255, year = {2020}, title = {{C}ounterfactual mean embeddings}, author = {{M}uandet, {K}rikamol and {K}anagawa, {M}otonobu and {S}aengkyongam, {S}orawit and {M}arukatat, {S}anparith}, booktitle = {{S}ubmitted to {A}r{X}i{V}, 1st {M}arch 2020}, address = {}, month = {03}, url = {} }
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