  The training-conditional coverage performance of the conformal prediction is
known to be empirically sound. Recently, there have been efforts to support
this observation with theoretical guarantees. The training-conditional coverage
bounds for jackknife+ and full-conformal prediction regions have been
established via the notion of $(m,n)$-stability by Liang and Barber~[2023].
Although this notion is weaker than uniform stability, it is not clear how to
evaluate it for practical models. In this paper, we study the
training-conditional coverage bounds of full-conformal, jackknife+, and CV+
prediction regions from a uniform stability perspective which is known to hold
for empirical risk minimization over reproducing kernel Hilbert spaces with
convex regularization. We derive coverage bounds for finite-dimensional models
by a concentration argument for the (estimated) predictor function, and compare
the bounds with existing ones under ridge regression.
