Evaluating and Correcting Performative Effects of Decision Support
  Systems via Causal Domain Shift
Philip Boeken Onno Zoeter Joris M. Mooij
When predicting a target variable $Y$ from features $X$, the prediction
$\hat{Y}$ can be performative: an agent might act on this prediction, affecting
the value of $Y$ that we eventually observe. Performative predictions are
deliberately prevalent in algorithmic decision support, where a Decision
Support System (DSS) provides a prediction for an agent to affect the value of
the target variable. When deploying a DSS in high-stakes settings (e.g.
healthcare, law, predictive policing, or child welfare screening) it is
imperative to carefully assess the performative effects of the DSS. In the case
that the DSS serves as an alarm for a predicted negative outcome, naive
retraining of the prediction model is bound to result in a model that
underestimates the risk, due to effective workings of the previous model. In
this work, we propose to model the deployment of a DSS as causal domain shift
and provide novel cross-domain identification results for the conditional
expectation $E[Y | X]$, allowing for pre- and post-hoc assessment of the
deployment of the DSS, and for retraining of a model that assesses the risk
under a baseline policy where the DSS is not deployed. Using a running example,
we empirically show that a repeated regression procedure provides a practical
framework for estimating these quantities, even when the data is affected by
sample selection bias and selective labelling, offering for a practical,
unified solution for multiple forms of target variable bias.