  Conformal prediction is a non-parametric technique for constructing
prediction intervals or sets from arbitrary predictive models under the
assumption that the data is exchangeable. It is popular as it comes with
theoretical guarantees on the marginal coverage of the prediction sets and the
split conformal prediction variant has a very low computational cost compared
to model training. We study the robustness of split conformal prediction in a
data contamination setting, where we assume a small fraction of the calibration
scores are drawn from a different distribution than the bulk. We quantify the
impact of the corrupted data on the coverage and efficiency of the constructed
sets when evaluated on "clean" test points, and verify our results with
numerical experiments. Moreover, we propose an adjustment in the classification
setting which we call Contamination Robust Conformal Prediction, and verify the
efficacy of our approach using both synthetic and real datasets.
