  A key condition for obtaining reliable estimates of the causal effect of a
treatment is overlap (a.k.a. positivity): the distributions of the features
used to perform causal adjustment cannot be too different in the treated and
control groups. In cases where overlap is poor, causal effect estimators can
become brittle, especially when they incorporate weighting. To address this
problem, a number of proposals (including confounder selection or dimension
reduction methods) incorporate feature representations to induce better overlap
between the treated and control groups. A key concern in these proposals is
that the representation may introduce confounding bias into the effect
estimator. In this paper, we introduce deconfounding scores, which are feature
representations that induce better overlap without biasing the target of
estimation. We show that deconfounding scores satisfy a zero-covariance
condition that is identifiable in observed data. As a proof of concept, we
characterize a family of deconfounding scores in a simplified setting with
Gaussian covariates, and show that in some simple simulations, these scores can
be used to construct estimators with good finite-sample properties. In
particular, we show that this technique could be an attractive alternative to
standard regularizations that are often applied to IPW and balancing weights.
