When one observes a sequence of variables $(x_1, y_1), ..., (x_n, y_n)$, conformal prediction 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. While appealing, the computation of such set turns out to be infeasible in general, e.g. when the unknown variable $y_{n+1}$ is continuous. In this paper, we combine conformal prediction techniques with algorithmic stability bounds to derive a prediction set computable with a single model fit. We perform some numerical experiments that illustrate the tightness of our estimation when the sample size is sufficiently large.
翻译:当人们观察一系列变量$(x_1, y_1, y_1,......, (x_n, y_n), 符合的预测是一种方法,可以仅仅假设数据的分布是可以交换的,从而估计对美元+1的置信度,给美元+1, 美元。 虽然有吸引力, 但这样的计算在总体上是行不通的, 例如当未知变量$@n+1是连续的。 在本文中, 我们将符合的预测技术与算法稳定性的界限结合起来, 得出一个可与单一模型兼容的预测集。 我们进行一些数字实验, 以说明当样本大小足够大时我们估算的紧凑性 。