The 50th Statistical Machine Learning Seminar
Organized by the Research Center for Statistical Machine Learning, The Institute of Statistical Mathematics
The 50th Statistical Machine Learning
Seminar
Date & Time: 16:00-17:30, September
27 (Tue)
Place: Zoom
Speaker: Motonobu Kanagawa (EURECOM)
Title: Counterfactual
Mean Embeddings
Abstract:
Counterfactual
inference has become ubiquitous in online advertisement, recommendation
systems, medical diagnosis, and econometrics. Accurate modeling of outcome
distributions associated with different interventions—known as counterfactual
distributions—is crucial for the success of these applications. We propose to
model counterfactual distributions using a novel Hilbert space representation
called counterfactual mean embedding (CME) in this work. 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) that can quantify the causal effect over entire outcome distributions.
Our approach is nonparametric as the CME can be estimated under the
unconfoundedness assumption 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 allows for more complex outcomes
such as images, sequences, and graphs. Our experimental results on synthetic
data and off-policy evaluation tasks demonstrate the advantages of the proposed
estimator