Résumé
Inferring causal effects of a treatment, intervention or policy from
observational data is central to many applications. However, state-of-the-art
methods for causal inference seldom consider the possibility that covariates
have missing values, which is ubiquitous in many real-world analyses. Missing
data greatly complicate causal inference procedures as they require an adapted
unconfoundedness hypothesis which can be difficult to justify in practice. We
circumvent this issue by considering latent confounders whose distribution is
learned through variational autoencoders adapted to missing values. They can be
used either as a pre-processing step prior to causal inference but we also
suggest to embed them in a multiple imputation strategy to take into account
the variability due to missing values. Numerical experiments demonstrate the
effectiveness of the proposed methodology especially for non-linear models
compared to competitors.