Survival Isotonic Distributional Regression

What the math gives to ML

The paper provides a constructive projection scheme for censored conditional distributions that repairs a failure of naive Kaplan-Meier pooling under heterogeneous groups. Its transferable asset is the cross-partition Cauchy mean value property: every interval estimate is clamped into bounds determined by all strict interval partitions, and the resulting recursion is guaranteed to be well-defined. This can serve as a statistically grounded calibration teacher or post-processing layer for neural survival models whose predictions should be monotone in an ordered covariate or learned risk score. The most practical first transfer is to distill S-IDR estimates computed on a held-out calibration set into a neural survival head, rather than attempting to backpropagate through the combinatorial recursion.