  Conformal prediction is a simple and powerful tool that can quantify
uncertainty without any distributional assumptions. Many existing methods only
address the average coverage guarantee, which is not ideal compared to the
stronger conditional coverage guarantee. Existing methods of approximating
conditional coverage require additional models or time effort, which makes them
not easy to scale. In this paper, we propose a modified non-conformity score by
leveraging the local approximation of the conditional distribution using kernel
density estimation. The modified score inherits the spirit of split conformal
methods, which is simple and efficient and can scale to high dimensional
settings. We also proposed a unified framework that brings together our method
and several state-of-the-art. We perform extensive empirical evaluations:
results measured by both average and conditional coverage confirm the advantage
of our method.
