  The deployment of safe and trustworthy machine learning systems, and
particularly complex black box neural networks, in real-world applications
requires reliable and certified guarantees on their performance. The conformal
prediction framework offers such formal guarantees by transforming any point
into a set predictor with valid, finite-set, guarantees on the coverage of the
true at a chosen level of confidence. Central to this methodology is the notion
of the nonconformity score function that assigns to each example a measure of
''strangeness'' in comparison with the previously seen observations. While the
coverage guarantees are maintained regardless of the nonconformity measure, the
point predictor and the dataset, previous research has shown that the
performance of a conformal model, as measured by its efficiency (the average
size of the predicted sets) and its informativeness (the proportion of
prediction sets that are singletons), is influenced by the choice of the
nonconformity score function. The current work introduces the Penalized Inverse
Probability (PIP) nonconformity score, and its regularized version RePIP, that
allow the joint optimization of both efficiency and informativeness. Through
toy examples and empirical results on the task of crop and weed image
classification in agricultural robotics, the current work shows how PIP-based
conformal classifiers exhibit precisely the desired behavior in comparison with
other nonconformity measures and strike a good balance between informativeness
and efficiency.
