We present and compare two new methods for generating prediction sets within the conformal prediction framework, each addressing the limitations of traditional approaches by targeting improved conditional coverage. The first method builds upon quantile regression to estimate the conditional quantile of conformity scores, which are then adjusted to account for local data structure. The second method integrates the flexibility of conformal methods with estimates of the conditional distribution label distribution​. By extending the framework of probabilistic conformal prediction, this approach achieves approximately conditional coverage through prediction sets that adapt effectively to the behavior of the predictive distribution, even under high heteroscedasticity. Non-asymptotic bounds are derived to quantify conditional coverage error for both approaches. Extensive simulations demonstrate that each method significantly improves over traditional techniques, paving the way for more robust and adaptable prediction set generation across diverse applications.
