When one observes a sequence of variables $(x_1, y_1), \ldots, (x_n, y_n)$,
Conformal Prediction (CP) is a methodology that allows to estimate a confidence
set for $y_{n+1}$ given $x_{n+1}$ by merely assuming that the distribution of
the data is exchangeable. CP sets have guaranteed coverage for any finite
population size $n$. While appealing, the computation of such a set turns out
to be infeasible in general, e.g. when the unknown variable $y_{n+1}$ is
continuous. The bottleneck is that it is based on a procedure that readjusts a
prediction model on data where we replace the unknown target by all its
possible values in order to select the most probable one. This requires
computing an infinite number of models, which often makes it intractable. In
this paper, we combine CP techniques with classical algorithmic stability
bounds to derive a prediction set computable with a single model fit. We
demonstrate that our proposed confidence set does not lose any coverage
guarantees while avoiding the need for data splitting as currently done in the
literature. We provide some numerical experiments to illustrate the tightness
of our estimation when the sample size is sufficiently large, on both synthetic
and real datasets.

本论文将 CP 技术与经典算法稳定性界限相结合，提出了一种置信区间集合，可用单一模型拟合计算，并证明了该方法能够保证精度，避免了数据分割的需求，成功解决了传统方法无法处理连续未知变量 y_n+1 的瓶颈问题。